From 9ce7bb7dbb6f8d7278ad24a997600981d885fb75 Mon Sep 17 00:00:00 2001 From: Kevin Jue Date: Sat, 17 Jun 2023 19:44:20 -0700 Subject: [PATCH] Step test case with public inputs (#23) * added step test case * export solidity code * just set proof's public input as public variables * make serialization a command line option * added flag to output solidity * some changes to the benchmark file * used gnark cherry picked bug fix * removed fuzz testing * added some logging * more debug messages and test cases for the hint issue * removed usage of goldilocks reduce * removed prints * removed GoldilocksReduce * removed prints * added a todo * some serialization changes --- benchmark.go | 86 +- field/goldilocks.go | 11 +- go.mod | 2 + go.sum | 2 - poseidon/poseidon.go | 20 +- poseidon/public_inputs_hash_test.go | 24 + verifier/data/step/common_circuit_data.json | 181 + .../data/step/proof_with_public_inputs.json | 16697 ++++++++++++++++ .../data/step/verifier_only_circuit_data.json | 21 + verifier/internal/plonk/plonk_test.go | 2 +- verifier/verifier.go | 36 +- verifier/verifier_test.go | 105 +- 12 files changed, 17093 insertions(+), 94 deletions(-) create mode 100644 verifier/data/step/common_circuit_data.json create mode 100644 verifier/data/step/proof_with_public_inputs.json create mode 100644 verifier/data/step/verifier_only_circuit_data.json diff --git a/benchmark.go b/benchmark.go index b48d3be..afa7bb8 100644 --- a/benchmark.go +++ b/benchmark.go @@ -6,22 +6,25 @@ import ( "os" "time" + "github.com/succinctlabs/gnark-plonky2-verifier/field" "github.com/succinctlabs/gnark-plonky2-verifier/verifier" "github.com/succinctlabs/gnark-plonky2-verifier/verifier/common" "github.com/succinctlabs/gnark-plonky2-verifier/verifier/utils" "github.com/consensys/gnark-crypto/ecc" "github.com/consensys/gnark/backend/groth16" + "github.com/consensys/gnark/constraint" "github.com/consensys/gnark/frontend" "github.com/consensys/gnark/frontend/cs/r1cs" "github.com/consensys/gnark/profile" ) type BenchmarkPlonky2VerifierCircuit struct { - ProofWithPis common.ProofWithPublicInputs `gnark:",public"` + Proof common.Proof + PublicInputs []field.F `gnark:",public"` - verifierChip *verifier.VerifierChip - plonky2CircuitName string + verifierChip *verifier.VerifierChip `gnark:"-"` + plonky2CircuitName string `gnark:"-"` } func (circuit *BenchmarkPlonky2VerifierCircuit) Define(api frontend.API) error { @@ -31,20 +34,21 @@ func (circuit *BenchmarkPlonky2VerifierCircuit) Define(api frontend.API) error { circuit.verifierChip = verifier.NewVerifierChip(api, commonCircuitData) - circuit.verifierChip.Verify(circuit.ProofWithPis, verifierOnlyCircuitData, commonCircuitData) + circuit.verifierChip.Verify(circuit.Proof, circuit.PublicInputs, verifierOnlyCircuitData, commonCircuitData) return nil } -func compileCircuit(plonky2Circuit string, doProfiling bool) { +func compileCircuit(plonky2Circuit string, profileCircuit bool, serialize bool, outputSolidity bool) (constraint.ConstraintSystem, groth16.ProvingKey, groth16.VerifyingKey) { circuit := BenchmarkPlonky2VerifierCircuit{ plonky2CircuitName: plonky2Circuit, } proofWithPis := utils.DeserializeProofWithPublicInputs("./verifier/data/" + plonky2Circuit + "/proof_with_public_inputs.json") - circuit.ProofWithPis = proofWithPis + circuit.Proof = proofWithPis.Proof + circuit.PublicInputs = proofWithPis.PublicInputs var p *profile.Profile - if doProfiling { + if profileCircuit { p = profile.Start() } r1cs, err := frontend.Compile(ecc.BN254.ScalarField(), r1cs.NewBuilder, &circuit) @@ -53,7 +57,7 @@ func compileCircuit(plonky2Circuit string, doProfiling bool) { os.Exit(1) } - if doProfiling { + if profileCircuit { p.Stop() p.Top() println("r1cs.GetNbCoefficients(): ", r1cs.GetNbCoefficients()) @@ -63,9 +67,14 @@ func compileCircuit(plonky2Circuit string, doProfiling bool) { println("r1cs.GetNbInternalVariables(): ", r1cs.GetNbInternalVariables()) } - fR1CS, _ := os.Create("circuit") - r1cs.WriteTo(fR1CS) - fR1CS.Close() + // Don't serialize the circuit for now, since it takes up too much memory + /* + if serialize { + fR1CS, _ := os.Create("circuit") + r1cs.WriteTo(fR1CS) + fR1CS.Close() + } + */ fmt.Println("Running circuit setup", time.Now()) pk, vk, err := groth16.Setup(r1cs) @@ -74,42 +83,37 @@ func compileCircuit(plonky2Circuit string, doProfiling bool) { os.Exit(1) } - fPK, _ := os.Create("proving.key") - pk.WriteTo(fPK) - fPK.Close() + if serialize { + fPK, _ := os.Create("proving.key") + pk.WriteTo(fPK) + fPK.Close() - fVK, _ := os.Create("verifying.key") - vk.WriteTo(fVK) - fVK.Close() + fVK, _ := os.Create("verifying.key") + vk.WriteTo(fVK) + fVK.Close() + } + + if outputSolidity { + fSolidity, _ := os.Create("proof.sol") + err = vk.ExportSolidity(fSolidity) + } + + return r1cs, pk, vk } -func createProof(plonky2Circuit string) groth16.Proof { +func createProof(plonky2Circuit string, r1cs constraint.ConstraintSystem, pk groth16.ProvingKey, vk groth16.VerifyingKey, serialize bool) groth16.Proof { proofWithPis := utils.DeserializeProofWithPublicInputs("./verifier/data/" + plonky2Circuit + "/proof_with_public_inputs.json") // Witness assignment := &BenchmarkPlonky2VerifierCircuit{ - ProofWithPis: proofWithPis, + Proof: proofWithPis.Proof, + PublicInputs: proofWithPis.PublicInputs, } fmt.Println("Generating witness", time.Now()) witness, _ := frontend.NewWitness(assignment, ecc.BN254.ScalarField()) publicWitness, _ := witness.Public() - r1cs := groth16.NewCS(ecc.BN254) - fR1CS, _ := os.Open("circuit") - r1cs.ReadFrom(fR1CS) - fR1CS.Close() - - var pk groth16.ProvingKey - fPK, _ := os.Open("proving.key") - pk.ReadFrom(fPK) - fPK.Close() - - var vk groth16.VerifyingKey - fVK, _ := os.Open("verifying.key") - vk.ReadFrom(fVK) - fVK.Close() - fmt.Println("Creating proof", time.Now()) proof, err := groth16.Prove(r1cs, pk, witness) if err != nil { @@ -123,12 +127,20 @@ func createProof(plonky2Circuit string) groth16.Proof { os.Exit(1) } + if serialize { + fProof, _ := os.Create("proof.proof") + proof.WriteTo(fProof) + } + return proof } func main() { plonky2Circuit := flag.String("plonky2-circuit", "", "plonky2 circuit to benchmark") - doProfile := flag.Bool("profile", false, "profile the circuit") + profileCircuit := flag.Bool("profile", false, "profile the circuit") + serialize := flag.Bool("serialize", false, "serialize the circuit") + outputSolidity := flag.Bool("solidity", false, "output solidity code for the circuit") + flag.Parse() if plonky2Circuit == nil || *plonky2Circuit == "" { @@ -136,6 +148,6 @@ func main() { os.Exit(1) } - compileCircuit(*plonky2Circuit, *doProfile) - createProof(*plonky2Circuit) + r1cs, pk, vk := compileCircuit(*plonky2Circuit, *profileCircuit, *serialize, *outputSolidity) + createProof(*plonky2Circuit, r1cs, pk, vk, *serialize) } diff --git a/field/goldilocks.go b/field/goldilocks.go index 4f4511c..4636578 100644 --- a/field/goldilocks.go +++ b/field/goldilocks.go @@ -165,12 +165,12 @@ func GoldilocksMulAdd(api frontend.API, operand1, operand2, operand3 frontend.Va func GoldilocksMulAddHint(_ *big.Int, inputs []*big.Int, results []*big.Int) error { if len(inputs) != 3 { - return fmt.Errorf("GoldilocksMulAddHint expects 3 input operands") + panic("GoldilocksMulAddHint expects 3 input operands") } for _, operand := range inputs { if operand.Cmp(GOLDILOCKS_MODULUS) >= 0 { - return fmt.Errorf("%s is not in the field", operand.String()) + panic(fmt.Sprintf("%s is not in the field", operand.String())) } } @@ -184,10 +184,3 @@ func GoldilocksMulAddHint(_ *big.Int, inputs []*big.Int, results []*big.Int) err return nil } - -func GoldilocksReduce(api frontend.API, x frontend.Variable) frontend.Variable { - // Use gnark's emulated field library. - fieldAPI := NewFieldAPI(api) - element := fieldAPI.NewElement(x) - return fieldAPI.Reduce(element).Limbs[0] -} diff --git a/go.mod b/go.mod index 02ea085..6e718e2 100644 --- a/go.mod +++ b/go.mod @@ -27,3 +27,5 @@ require ( gopkg.in/yaml.v3 v3.0.1 // indirect rsc.io/tmplfunc v0.0.3 // indirect ) + +replace github.com/consensys/gnark => /Users/kevin/succinctlabs/gnark diff --git a/go.sum b/go.sum index 109bf9c..309223d 100644 --- a/go.sum +++ b/go.sum @@ -2,8 +2,6 @@ github.com/blang/semver/v4 v4.0.0 h1:1PFHFE6yCCTv8C1TeyNNarDzntLi7wMI5i/pzqYIsAM github.com/blang/semver/v4 v4.0.0/go.mod h1:IbckMUScFkM3pff0VJDNKRiT6TG/YpiHIM2yvyW5YoQ= github.com/consensys/bavard v0.1.13 h1:oLhMLOFGTLdlda/kma4VOJazblc7IM5y5QPd2A/YjhQ= github.com/consensys/bavard v0.1.13/go.mod h1:9ItSMtA/dXMAiL7BG6bqW2m3NdSEObYWoH223nGHukI= -github.com/consensys/gnark v0.8.0 h1:0bQ2MyDG4oNjMQpNyL8HjrrUSSL3yYJg0Elzo6LzmcU= -github.com/consensys/gnark v0.8.0/go.mod h1:aKmA7dIiLbTm0OV37xTq0z+Bpe4xER8EhRLi6necrm8= github.com/consensys/gnark-crypto v0.9.1 h1:mru55qKdWl3E035hAoh1jj9d7hVnYY5pfb6tmovSmII= github.com/consensys/gnark-crypto v0.9.1/go.mod h1:a2DQL4+5ywF6safEeZFEPGRiiGbjzGFRUN2sg06VuU4= github.com/coreos/go-systemd/v22 v22.3.3-0.20220203105225-a9a7ef127534/go.mod h1:Y58oyj3AT4RCenI/lSvhwexgC+NSVTIJ3seZv2GcEnc= diff --git a/poseidon/poseidon.go b/poseidon/poseidon.go index 9179802..ad4ef69 100644 --- a/poseidon/poseidon.go +++ b/poseidon/poseidon.go @@ -172,12 +172,11 @@ func (c *PoseidonChip) mdsRowShf(r int, v [SPONGE_WIDTH]frontend.Variable) front for i := 0; i < 12; i++ { if i < SPONGE_WIDTH { - res1 := c.api.Mul(v[(i+r)%SPONGE_WIDTH], MDS_MATRIX_CIRC_VARS[i]) - res = c.api.Add(res, res1) + res = field.GoldilocksMulAdd(c.api, v[(i+r)%SPONGE_WIDTH], MDS_MATRIX_CIRC_VARS[i], res) } } - res = c.api.Add(res, c.api.Mul(v[r], MDS_MATRIX_DIAG_VARS[r])) + res = field.GoldilocksMulAdd(c.api, v[r], MDS_MATRIX_DIAG_VARS[r], res) return res } @@ -203,15 +202,9 @@ func (c *PoseidonChip) mdsLayer(state_ PoseidonState) PoseidonState { result[i] = frontend.Variable(0) } - var state [SPONGE_WIDTH]frontend.Variable - for i := 0; i < SPONGE_WIDTH; i++ { - state[i] = field.GoldilocksReduce(c.api, state_[i]) - } - for r := 0; r < 12; r++ { if r < SPONGE_WIDTH { - sum := c.mdsRowShf(r, state) - result[r] = field.GoldilocksReduce(c.api, sum) + result[r] = c.mdsRowShf(r, state_) } } @@ -298,14 +291,11 @@ func (c *PoseidonChip) mdsPartialLayerFast(state PoseidonState, r int) PoseidonS for i := 1; i < 12; i++ { if i < SPONGE_WIDTH { t := FAST_PARTIAL_ROUND_W_HATS_VARS[r][i-1] - reducedState := field.GoldilocksReduce(c.api, state[i]) - dSum = c.api.Add(dSum, c.api.Mul(reducedState, t)) + dSum = field.GoldilocksMulAdd(c.api, state[i], t, dSum) } } - s0 := field.GoldilocksReduce(c.api, state[0]) - dSum = c.api.Add(dSum, c.api.Mul(s0, MDS0TO0_VAR)) - d := field.GoldilocksReduce(c.api, dSum) + d := field.GoldilocksMulAdd(c.api, state[0], MDS0TO0_VAR, dSum) var result PoseidonState for i := 0; i < SPONGE_WIDTH; i++ { diff --git a/poseidon/public_inputs_hash_test.go b/poseidon/public_inputs_hash_test.go index c27d70f..354965e 100644 --- a/poseidon/public_inputs_hash_test.go +++ b/poseidon/public_inputs_hash_test.go @@ -4,6 +4,7 @@ import ( "testing" "github.com/consensys/gnark-crypto/ecc" + "github.com/consensys/gnark/backend" "github.com/consensys/gnark/frontend" "github.com/consensys/gnark/test" "github.com/succinctlabs/gnark-plonky2-verifier/field" @@ -58,3 +59,26 @@ func TestPublicInputsHashWitness(t *testing.T) { copy(out[:], utils.StrArrayToFrontendVariableArray(outStr)) testCase(in, out) } + +func TestPublicInputsHashWitness2(t *testing.T) { + assert := test.NewAssert(t) + + inStr := []string{"0", "1", "3736710860384812976"} + outStr := []string{"8416658900775745054", "12574228347150446423", "9629056739760131473", "3119289788404190010"} + var in [3]frontend.Variable + var out [4]frontend.Variable + copy(in[:], utils.StrArrayToFrontendVariableArray(inStr)) + copy(out[:], utils.StrArrayToFrontendVariableArray(outStr)) + + circuit := TestPublicInputsHashCircuit{In: in, Out: out} + witness := TestPublicInputsHashCircuit{In: in, Out: out} + + assert.ProverSucceeded( + &circuit, + &witness, + test.WithBackends(backend.GROTH16), + test.WithCurves(ecc.BN254), + test.NoFuzzing(), + test.NoSerialization(), + ) +} diff --git a/verifier/data/step/common_circuit_data.json b/verifier/data/step/common_circuit_data.json new file mode 100644 index 0000000..ef75db8 --- /dev/null +++ b/verifier/data/step/common_circuit_data.json @@ -0,0 +1,181 @@ +{ + "config": { + "num_wires": 136, + "num_routed_wires": 80, + "num_constants": 2, + "use_base_arithmetic_gate": true, + "security_bits": 100, + "num_challenges": 2, + "zero_knowledge": false, + "max_quotient_degree_factor": 8, + "fri_config": { + "rate_bits": 3, + "cap_height": 4, + "proof_of_work_bits": 16, + "reduction_strategy": { + "ConstantArityBits": [ + 4, + 5 + ] + }, + "num_query_rounds": 28 + } + }, + "fri_params": { + "config": { + "rate_bits": 3, + "cap_height": 4, + "proof_of_work_bits": 16, + "reduction_strategy": { + "ConstantArityBits": [ + 4, + 5 + ] + }, + "num_query_rounds": 28 + }, + "hiding": false, + "degree_bits": 13, + "reduction_arity_bits": [ + 4, + 4 + ] + }, + "gates": [ + "NoopGate", + "PoseidonMdsGate(PhantomData)", + "PublicInputGate", + "BaseSumGate { num_limbs: 63 } + Base: 2", + "ReducingExtensionGate { num_coeffs: 33 }", + "ReducingGate { num_coeffs: 44 }", + "ArithmeticExtensionGate { num_ops: 10 }", + "ArithmeticGate { num_ops: 20 }", + "MulExtensionGate { num_ops: 13 }", + "ExponentiationGate { num_power_bits: 67, _phantom: PhantomData }", + "RandomAccessGate { bits: 4, num_copies: 4, num_extra_constants: 2, _phantom: PhantomData }", + "CosetInterpolationGate { subgroup_bits: 4, degree: 6, barycentric_weights: [17293822565076172801, 18374686475376656385, 18446744069413535745, 281474976645120, 17592186044416, 18446744069414584577, 18446744000695107601, 18446744065119617025, 1152921504338411520, 72057594037927936, 18446744069415632897, 18446462594437939201, 18446726477228539905, 18446744069414584065, 68719476720, 4294967296], _phantom: PhantomData }", + "PoseidonGate(PhantomData)" + ], + "selectors_info": { + "selector_indices": [ + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 1, + 1, + 1, + 2, + 2, + 3 + ], + "groups": [ + { + "start": 0, + "end": 6 + }, + { + "start": 6, + "end": 10 + }, + { + "start": 10, + "end": 12 + }, + { + "start": 12, + "end": 13 + } + ] + }, + "quotient_degree_factor": 8, + "num_gate_constraints": 123, + "num_constants": 6, + "num_public_inputs": 1350, + "k_is": [ + 1, + 7, + 49, + 343, + 2401, + 16807, + 117649, + 823543, + 5764801, + 40353607, + 282475249, + 1977326743, + 13841287201, + 96889010407, + 678223072849, + 4747561509943, + 33232930569601, + 232630513987207, + 1628413597910449, + 11398895185373143, + 79792266297612001, + 558545864083284007, + 3909821048582988049, + 8922003270666332022, + 7113790686420571191, + 12903046666114829695, + 16534350385145470581, + 5059988279530788141, + 16973173887300932666, + 8131752794619022736, + 1582037354089406189, + 11074261478625843323, + 3732854072722565977, + 7683234439643377518, + 16889152938674473984, + 7543606154233811962, + 15911754940807515092, + 701820169165099718, + 4912741184155698026, + 15942444219675301861, + 916645121239607101, + 6416515848677249707, + 8022122801911579307, + 814627405137302186, + 5702391835961115302, + 3023254712898638472, + 2716038920875884983, + 565528376716610560, + 3958698637016273920, + 9264146389699333119, + 9508792519651578870, + 11221315429317299127, + 4762231727562756605, + 14888878023524711914, + 11988425817600061793, + 10132004445542095267, + 15583798910550913906, + 16852872026783475737, + 7289639770996824233, + 14133990258148600989, + 6704211459967285318, + 10035992080941828584, + 14911712358349047125, + 12148266161370408270, + 11250886851934520606, + 4969231685883306958, + 16337877731768564385, + 3684679705892444769, + 7346013871832529062, + 14528608963998534792, + 9466542400916821939, + 10925564598174000610, + 2691975909559666986, + 397087297503084581, + 2779611082521592067, + 1010533508236560148, + 7073734557655921036, + 12622653764762278610, + 14571600075677612986, + 9767480182670369297 + ], + "num_partial_products": 9 +} diff --git a/verifier/data/step/proof_with_public_inputs.json b/verifier/data/step/proof_with_public_inputs.json new file mode 100644 index 0000000..7c6680a --- /dev/null +++ b/verifier/data/step/proof_with_public_inputs.json @@ -0,0 +1,16697 @@ +{ + "proof": { + "wires_cap": [ + "6786621447802187425798400955463754435905422407674569040607616827009343601991", + "8888439531382224969342124289058187350813381908100247734589925861413661126469", + "17612769911487390337282225803219906691056432756347082104387302432965955616246", + "18644586406684964264186422530615641999453043261521004587367358944051842921639", + "8364014899437285893780632088933883682895318812070028723496790966355897076275", + "20840826563202759815290267720522359482238447459651851933295171536282018603808", + "20925235521821902912167078470754725290935221225158677316431795377930707546628", + "10465252578559430001817629514869848479341361696523278178345548163362993013578", + "2487352707407471655173548521709939663127694224386572844680159991489632817102", + "15079893798094942333275790805889464115884391347302954076453655560337549427473", + "11555936865808834819761392234648557861114382613460672593091986095565531955530", + "19811249628568751762685977516379321763270539661727746397006168525787614711117", + "16907690093643617491707200490874594337572865635174719829485677809200796192916", + "11149574181875705213791760189242331839997074246491516355043814737162741013516", + "5156451258465954951970351244747820954233227780241803438920673110316991339497", + "13746285583181586360718863872251740543677443658833904856416531754853919939076" + ], + "plonk_zs_partial_products_cap": [ + "305928305907397886134112668967290932438734704622841683704361078357534581682", + "4057785853723303556984176663306314477994839847095719019736482328758526242267", + "5156748670451173327779830821178501767150914755895466232435549257789790065218", + "6071871147187997976919770261155076834251286079212981138169843047628490557837", + "19760788498694337192163189684482455919758122757726987859135745322470687532421", + "3438137180572030730548136974540116002794202757689261136723447053279157414687", + "17154011657769926394300982113275745445017787337546134600428152890602506400367", + "1234381809112120948765868846371351455384047520600000113467098788284508917423", + "7679719273086499594141779699202526952341747383462044488733052731152670150627", + "13580770380931715411747296597928248282046397550182864281181986356427071224177", + "9747693148737767652941500953581301017985685220454037594533488953818913496717", + "15520143827698179742926554862975252233067549827638453378756632649391663988458", + "16607746110850819385318634062976550633967855982697069716372158228890486827726", + "7755943914876096453114487862078453399495523617759094130438099660838565309374", + "19157082246078473240317748320617063991600636849107136615452884458747302852081", + "17648505806272663674965415037624595760890714215106438948810414252881910004763" + ], + "quotient_polys_cap": [ + "18968626405535488315427676256572406905685870034571230646943525354171657487977", + "20718388728455356892242698889826928576606724367209817160291461394913824999873", + "12742225504897168201986877867929646697531571360025269568627783979261887901918", + "12209450327427073020873730476320193345292735315026810009208009508125597894337", + "1018421267807334853024880882804556356951997118271054554700700154360809822412", + "3726430449817368990533921316953828459583074846131752684580872691583148965203", + "8059534524567210218209384283382867422177344607247567907622528082948370735305", + "20197360726979646733048911886585107222172034968609058015093548178005570117759", + "9273440202101178900734425278995657800657794960786097220205485173676233133040", + "7306941536054881856096408180423820506028935386404119008848294015365793956657", + "19776720125380652007576608556913939502722301934964432563120282543808784120270", + "5058091805298105609858840774340680496448028369819341686409824665643041193738", + "13543516464970341348855249982821855667864247714544661221953028462181892358875", + "4398921832338036494206504677359623012173522173382478807587978466136426737642", + "10872610321616322515139660717914090004702299073987049841780778133438378513076", + "17784607935308450892988641086249315815260796039548459726515190906078624389144" + ], + "openings": { + "constants": [ + [ + 7450292191990619094, + 1262279576317028262 + ], + [ + 4006530145677480971, + 6971733990092756612 + ], + [ + 18270835532879188107, + 3592249009624753209 + ], + [ + 15198746153162442298, + 5999061999778893577 + ], + [ + 4810092516530228376, + 4519629300557862033 + ], + [ + 2480477079742463849, + 6783021817616697579 + ] + ], + "plonk_sigmas": [ + [ + 12238040497925227662, + 17423394943869959206 + ], + [ + 8887316668372023536, + 4621865710731590186 + ], + [ + 12309705634772221685, + 13760471492401807529 + ], + [ + 8630744369223626342, + 3286850839866126402 + ], + [ + 15294297887343385451, + 16262218359254521883 + ], + [ + 9199542052135524433, + 17788271184969303741 + ], + [ + 8684159828162392137, + 10461364437828075321 + ], + [ + 2854915179455287628, + 9761493665367054764 + ], + [ + 9103107532360405987, + 2926546979735566684 + ], + [ + 12747926059302897158, + 12062267485643599232 + ], + [ + 3138305854781362047, + 16206830613718664631 + ], + [ + 5375948829087074121, + 262820289501364142 + ], + [ + 11006524091110218668, + 3925079550746389309 + ], + [ + 7322311983714387063, + 14070997653417281735 + ], + [ + 13919956105365375178, + 4554057208798073774 + ], + [ + 5282717636807010663, + 18266821188161173335 + ], + [ + 10530707221170672228, + 13934574876589475715 + ], + [ + 9507717768751186225, + 549387955994240051 + ], + [ + 12900932294080315512, + 361677358992157219 + ], + [ + 10694540899031055902, + 11634221342543703054 + ], + [ + 16108121674512804150, + 5801510677116422004 + ], + [ + 1868765888886473130, + 14492535691736128142 + ], + [ + 14310306441684060015, + 9759644283803029201 + ], + [ + 3337241471497246755, + 13438148657869124460 + ], + [ + 6212942332580889571, + 3744305507213546964 + ], + [ + 917793943213967479, + 4218304677839013387 + ], + [ + 9744723712736860925, + 6931373339998647055 + ], + [ + 17874816877080204278, + 12535993144986773638 + ], + [ + 32510867499256848, + 10444061910201993897 + ], + [ + 7707677574289228299, + 17850579208831901804 + ], + [ + 17890853154978888994, + 11779646958748385425 + ], + [ + 17850292589717337500, + 3092460646205374649 + ], + [ + 8113143572963796299, + 8156409740275225821 + ], + [ + 11017551073186879142, + 15478022998760223950 + ], + [ + 14006604710134395322, + 1321345168480377259 + ], + [ + 8300163319112522827, + 2927184794551999952 + ], + [ + 2820608222046545011, + 5881954908033623051 + ], + [ + 12975201042070587357, + 7493330110257350872 + ], + [ + 2010762347475770379, + 5239503932596307064 + ], + [ + 11505551403845299437, + 14548432382448767754 + ], + [ + 9381993499346120710, + 15853509751220876404 + ], + [ + 7379398024452986740, + 2945065814341683422 + ], + [ + 7272149705826243376, + 16430593036237977726 + ], + [ + 6487972182210459239, + 785339342481260995 + ], + [ + 840927957865953963, + 13434590765657610713 + ], + [ + 10217376309884296310, + 2843654515938312624 + ], + [ + 8270267394326097548, + 9208791379020002050 + ], + [ + 4039071583891376897, + 1502056886593289936 + ], + [ + 13023778802573027739, + 2752148915425738393 + ], + [ + 8753674302944596493, + 13723583985205175554 + ], + [ + 17514048704002074399, + 10195773267276514587 + ], + [ + 83008457111439810, + 16659677645849347014 + ], + [ + 12937282395802206835, + 7449926795326038194 + ], + [ + 12975874792984047361, + 11031636949414354200 + ], + [ + 10977598817002624319, + 16050760893806920277 + ], + [ + 10143851775193979063, + 11877371299479575410 + ], + [ + 16061798344613839354, + 14735159601695219791 + ], + [ + 12603185181829725530, + 17781515068021681792 + ], + [ + 13941707193964172229, + 7043007363996107427 + ], + [ + 91630847523649921, + 15210936217997795246 + ], + [ + 5683654914552729235, + 5055274078884411362 + ], + [ + 8325614505862303029, + 9045980965671347501 + ], + [ + 13648699576748574881, + 5457953480152138621 + ], + [ + 1246980027675888544, + 17293702753571421166 + ], + [ + 2989376539233512178, + 11793659934834567995 + ], + [ + 4091281166767772725, + 11763088679227056051 + ], + [ + 7578929063801967219, + 6916318420438817130 + ], + [ + 9034994071637846300, + 7141773876092891359 + ], + [ + 6694137140324214959, + 997000969694122662 + ], + [ + 9329053659140015027, + 470881846396938419 + ], + [ + 9715580137210711278, + 5854402935341321504 + ], + [ + 3287998774648895421, + 17113834079930745536 + ], + [ + 4000961078294965372, + 7323964054679909291 + ], + [ + 4284069754569373930, + 2617547585824473089 + ], + [ + 9721480451743602302, + 3160345824025158211 + ], + [ + 166468597988509815, + 11588601186918660379 + ], + [ + 9908786691798231427, + 9902531096539759889 + ], + [ + 4288275865659175762, + 4858404939779686353 + ], + [ + 6453317819469529706, + 17175310288967097601 + ], + [ + 16164860709164284192, + 14372738168358282939 + ] + ], + "wires": [ + [ + 8030131495810934714, + 2071966435627956878 + ], + [ + 12310684904994297651, + 6824173139598433422 + ], + [ + 11879798928716662433, + 12008430170405771716 + ], + [ + 3379341029452885569, + 9939537551772357857 + ], + [ + 10952220036709142623, + 14736087568001395475 + ], + [ + 7813825799628916847, + 560555130895057117 + ], + [ + 2044001574036070485, + 13838665373659354728 + ], + [ + 6288370631591384497, + 14014867450687346881 + ], + [ + 12757867458528254968, + 13813782984118204453 + ], + [ + 17376422336876318557, + 13272974256842850712 + ], + [ + 765974788589599518, + 6924419174457851126 + ], + [ + 2374294215708725823, + 7262388876616659929 + ], + [ + 10731285012893260985, + 9345458057890388559 + ], + [ + 12833650141160316838, + 1861769004300671709 + ], + [ + 8824927657926517076, + 14702039958514736567 + ], + [ + 8498543250104452959, + 14043187883518312173 + ], + [ + 1256849428782236751, + 14255566966150917611 + ], + [ + 455521710567629872, + 14034947782080370559 + ], + [ + 16953832104755900573, + 10503930882656338776 + ], + [ + 14573256839721465712, + 10415924508009726665 + ], + [ + 5033559380773027988, + 16934467362432699195 + ], + [ + 15808125454963403919, + 2273563941770510054 + ], + [ + 6757812996050531684, + 11257062662379394096 + ], + [ + 12065018383898453156, + 10034923230160347840 + ], + [ + 1014810807675996075, + 17365872575467739428 + ], + [ + 5785172220061685695, + 7150183223647346896 + ], + [ + 15307580280226198467, + 1421428266217185305 + ], + [ + 8708850534751677930, + 9500594571598964570 + ], + [ + 6768297759181336906, + 13690530001710006722 + ], + [ + 17912770476270346857, + 9326465438735996455 + ], + [ + 16000902555927092989, + 4340476548045292749 + ], + [ + 4343201804855797608, + 14898415431701777588 + ], + [ + 4220841602508383453, + 13467862057004744749 + ], + [ + 15922674333936246032, + 6562090085196553921 + ], + [ + 686667279624616851, + 9295079176432720570 + ], + [ + 15111432799428784791, + 17503699155127794239 + ], + [ + 15221383877121437333, + 17402223106853208447 + ], + [ + 8474420036337943251, + 11113116845402686472 + ], + [ + 1303295223370257131, + 15999930864521061021 + ], + [ + 9186969003511031609, + 10454400111844891016 + ], + [ + 2827601809746948510, + 13965991989782837036 + ], + [ + 14914729809946227579, + 14802791930509075714 + ], + [ + 14384715540489319047, + 14280327257760943588 + ], + [ + 4930755948357199098, + 2620309676862728942 + ], + [ + 14256786075646172105, + 8367945996187218548 + ], + [ + 13706107637892174619, + 7171528715700343462 + ], + [ + 16225074415062226531, + 13721771438516989283 + ], + [ + 4958930121471716441, + 3036650759117528237 + ], + [ + 7186018915635534401, + 10015058897920652407 + ], + [ + 6149742944770778590, + 2839556944494693228 + ], + [ + 17735819327631801798, + 3946900163440871023 + ], + [ + 9127914222661913134, + 7166524136402586431 + ], + [ + 14930044672880197887, + 413976083407489261 + ], + [ + 8655722323347112105, + 8568440711919646182 + ], + [ + 17343289245262034974, + 4798558071018084143 + ], + [ + 2821319192722133047, + 1258367626151143108 + ], + [ + 8146180616451858086, + 3647727655735112456 + ], + [ + 3193870506639597329, + 11664208355585265501 + ], + [ + 2928213420504769830, + 1061010272867847790 + ], + [ + 14654832522399324248, + 17869715606759617057 + ], + [ + 10019745650664090530, + 10061464948614184567 + ], + [ + 8162413460357108204, + 7477511186980535683 + ], + [ + 7774979624306927774, + 8391602435941286987 + ], + [ + 5086153572164454104, + 10011386950241896552 + ], + [ + 10959931972568454666, + 15335640861374970025 + ], + [ + 7997275688815307000, + 11179138547743974611 + ], + [ + 8185509817276570964, + 10862557495339244990 + ], + [ + 7894077652236165995, + 11718876253447237498 + ], + [ + 12829634309263678293, + 16406919017283931663 + ], + [ + 8317658705997180757, + 12563970411875195484 + ], + [ + 6579840626528158073, + 16935120078364836386 + ], + [ + 5535344672874723097, + 3379398168008828509 + ], + [ + 17409680092939014014, + 2141140366159717971 + ], + [ + 13634657494136851814, + 5228636246250229675 + ], + [ + 13426736032791716800, + 7610477975156942820 + ], + [ + 17490622230763962417, + 800856803535506928 + ], + [ + 6695164758236231480, + 14579872443916023397 + ], + [ + 10141422375733027887, + 16735799701479381771 + ], + [ + 13573254186957532420, + 13788406343561119312 + ], + [ + 18096270047646827140, + 18292711552637875834 + ], + [ + 9295551917508293705, + 18298440753475066150 + ], + [ + 2468135982548101961, + 4773313169779248070 + ], + [ + 10657216772769937322, + 8684148026750621876 + ], + [ + 9840355688455028977, + 1100997038515072941 + ], + [ + 8445061746781051022, + 1031647560724394756 + ], + [ + 5167945882382697674, + 17720530823672910345 + ], + [ + 888632250366785833, + 8637206950167220854 + ], + [ + 5618817638942760437, + 1250960696522510911 + ], + [ + 17845159477936308177, + 5421601387342610572 + ], + [ + 14580095968307987753, + 15256701084437772500 + ], + [ + 11129570382033874624, + 7780205693745885330 + ], + [ + 1199244753207254618, + 10229562603382571519 + ], + [ + 18231241232926949667, + 13941350558202514431 + ], + [ + 9883586288829276523, + 14537637390459923958 + ], + [ + 9542935602124330316, + 12153201324479394092 + ], + [ + 1968951912646592185, + 4770732836986838055 + ], + [ + 17212446789919016982, + 13257683378657631513 + ], + [ + 1232445978965437778, + 15603736997053353514 + ], + [ + 12935726348183669985, + 4018647012572394617 + ], + [ + 5139593702429964398, + 11008034788513002123 + ], + [ + 11887146750221425076, + 12629713220447712247 + ], + [ + 14624631078256368859, + 4816284559613817010 + ], + [ + 4305933141434538719, + 13039009769768630159 + ], + [ + 13303198189084810062, + 687460195955282456 + ], + [ + 4292297898521293187, + 12944504705119862748 + ], + [ + 2311908616195884534, + 10713109577907844965 + ], + [ + 832089711624034777, + 10734474823882099597 + ], + [ + 9169413200696754766, + 12507240682136999095 + ], + [ + 2867307364018109041, + 4049285702637430522 + ], + [ + 4313497809090276320, + 18173276881608305563 + ], + [ + 10179301561151872404, + 785365330532484528 + ], + [ + 4060091824764373141, + 4351214774589952583 + ], + [ + 13289986821171902685, + 8428096753581660795 + ], + [ + 13254540023288769665, + 6231686950613821171 + ], + [ + 5648622334025107198, + 8328809360419408095 + ], + [ + 11408804365802299871, + 3490307057099279551 + ], + [ + 11654135676479497807, + 15062883513062999335 + ], + [ + 1906930414879177161, + 4993217308645991174 + ], + [ + 3477282703808421737, + 6731984012935663339 + ], + [ + 4484549169784726997, + 15822092048029702451 + ], + [ + 3813708073758960048, + 7921982583093826138 + ], + [ + 1246181194868583207, + 10375338985313916338 + ], + [ + 5330179018614836433, + 12689833853827909155 + ], + [ + 3373769401752293606, + 7318949734786244124 + ], + [ + 10380877846137221461, + 14151431757414305871 + ], + [ + 9240316929742101063, + 9079148700720915483 + ], + [ + 9163366510712011934, + 3548636941841485888 + ], + [ + 8687473582988199606, + 18220358255827840763 + ], + [ + 8711336355901230972, + 908653202909772864 + ], + [ + 1897008037981519156, + 14436975771960132185 + ], + [ + 13847913117060358275, + 11562774495873128778 + ], + [ + 5330892452853502380, + 2661438821610229884 + ], + [ + 16484504584596508560, + 3057827650684413740 + ], + [ + 17872446457825486790, + 1430399393498451154 + ], + [ + 11306703168824803791, + 5376700197909727801 + ], + [ + 2984645875420120845, + 13691449204368326641 + ] + ], + "plonk_zs": [ + [ + 7394120914357079687, + 14237204176593096097 + ], + [ + 1642232304414603221, + 3676687301262403549 + ] + ], + "plonk_zs_next": [ + [ + 13181314388723719821, + 12486303207421392703 + ], + [ + 9872768150571659264, + 5061740706854369244 + ] + ], + "partial_products": [ + [ + 2272184160842091283, + 14325875233790095232 + ], + [ + 7925165161173701610, + 458836754628992222 + ], + [ + 9465361003302232576, + 17920221588096791903 + ], + [ + 6661510588780757770, + 17407852374243083525 + ], + [ + 9574376259981781580, + 17005275924146812535 + ], + [ + 11593060897879066517, + 8781313443019824742 + ], + [ + 8041292639075856834, + 6898696158333157810 + ], + [ + 12849563386355032890, + 784507974965442361 + ], + [ + 9501374221169713851, + 1834243950909673916 + ], + [ + 15981411575164130103, + 9801447486879276900 + ], + [ + 14125869682522593772, + 13884921512942410760 + ], + [ + 10562814976560357474, + 3342619042562348209 + ], + [ + 16321371901058733676, + 15891303841188441801 + ], + [ + 15141008893322609220, + 10375818466188917358 + ], + [ + 6871017938659776003, + 17522748674141834454 + ], + [ + 4379345093148866052, + 488015984784791209 + ], + [ + 1257336566045132562, + 6567986826881346745 + ], + [ + 13533317400438820713, + 6431692584931654076 + ] + ], + "quotient_polys": [ + [ + 18020848222817659877, + 855048548524044426 + ], + [ + 14149232808743111977, + 10813493236238510756 + ], + [ + 1908945378757572302, + 13558014319509523248 + ], + [ + 15519203106855154263, + 3796614690641075251 + ], + [ + 10587213548377347473, + 9411379450193779562 + ], + [ + 8585730798111733256, + 13625792826527601817 + ], + [ + 13788259978753829200, + 10669747944067497492 + ], + [ + 6703967568573109368, + 201544717488086224 + ], + [ + 531076437849576391, + 11613334074901606874 + ], + [ + 17244234598941731843, + 15260537174508496525 + ], + [ + 9072395542532593781, + 7748911368253394436 + ], + [ + 7688963376927626037, + 15681379586670703528 + ], + [ + 2671399424675708082, + 14939704122804738767 + ], + [ + 15887781656504201933, + 3011387306600566686 + ], + [ + 15069380046366134390, + 14561287115525015801 + ], + [ + 36728283581694385, + 10074158058962014460 + ] + ] + }, + "opening_proof": { + "commit_phase_merkle_caps": [ + [ + "15555523050659778769646128432872916068390510397420667644996167798843131144516", + "8190798472239709138915015327922408569071145972766971332581808318044003204888", + "2062272374318357197095290611043663648468144392662811619466997047071762422825", + "5595181956708309207609843066702944033426613253314859602261785019598680693696", + "12231327296752696889664080349688427598375877110287834961702270628466616023520", + "15423041246145447997618304802426009290475480749819443263553159460008102921357", + "1846414528331639929149929382253002567491766189276475326086382633173401886563", + "965342417095239043799977205975103275981969337537619645924499453258545383034", + "20145934149705331882393221746585794884187255004366526707613993423708683392932", + "9075642305530702308571353686013305648462998867655024156164660605324376708177", + "5683105929542736406412185029360392649229204011693430977141672381826259767982", + "17644625248871982075069025661400778320202491522396378162242166061167193916474", + "4325395170435555021225013282861870661823812546179789451104642301318592500335", + "7809276461857643077502611551071349374823410842584510045907780907732163356470", + "4251090075698729687070046103134333885850575335911132298646121613691556068161", + "481096144456567138149473076283883218094938237595982192295137581860947100752" + ], + [ + "16757225754419893902778338527237780445640267392499507993862890067652235851921", + "19841529593736744693517475897993560917551034940782376418129185161280617476216", + "9466286338035667867789819093943096195627625377178658238879274940723342978356", + "5300910510500976133963265715394296644540444998893742017702342000633288817806", + "4444792141416486389885434127489152779026756523626801828581705089620387469819", + "13833007264502559285891889248202071423603444602076664063799860819951769244451", + "6314060307548360679651088746227424991506495651978382402025263717694288736249", + "20111129982895400919018147419319378775474666179160526677367941429258872844757", + "5116213614533624220999110930365694696758925901013615727334572057081458280849", + "15917473169181685680119705974729296127518920366019978565681091208845572826685", + "13052982149984971633737256449112445818016961608514874947639813030782753727484", + "64094869648071090203244672187676438141148287065252033847427472666222314615", + "12355647416702515791768585613381700606011167092863399006419297580610355135021", + "14242154131095760700928673551466072032464117928125540362895610250944120724199", + "9405295314383940733759554477173684684247967669138731746104441946528661121835", + "2483114702512749926843084633276019801123281885463571062840575518148091484133" + ] + ], + "query_round_proofs": [ + { + "initial_trees_proof": { + "evals_proofs": [ + [ + [ + 10570728808082619023, + 16995300025693530479, + 10205513971333852410, + 17693701439157224605, + 16486780346734473988, + 4829694891429605604, + 13149401086361394995, + 7564754370837195598, + 13489285484808408951, + 13232210714050252900, + 13868996812700449147, + 14201263622663307048, + 17502344688974563903, + 11297474024673404588, + 7154179426755935424, + 13376258249214583522, + 7445672317476187155, + 8180261412190159135, + 5835035964173770785, + 2189878722830897208, + 706065472520773765, + 13246760097732223811, + 1432842723865857610, + 5102253960255412210, + 17866362470540564575, + 7068219870588114978, + 12838854124466364205, + 6505798473005721588, + 17968003491315539521, + 14391560599062154111, + 11531887849916638971, + 9478417633113434736, + 4793550184057383604, + 17060020618106063064, + 1775509271826360587, + 12722540876455937416, + 16595718076203755791, + 3918888774076621537, + 16733372780744489294, + 18391541891446384603, + 10926661996831737976, + 13676664418232872557, + 4705121979182484369, + 2342040911822735524, + 7699400084407220059, + 1652818683860118815, + 3822916159774529670, + 18001719409426811700, + 5198833670060347504, + 10453133512115016540, + 13632213424523443644, + 15105461868939720858, + 11982524342510167125, + 4848266980303161185, + 11353198763221484267, + 8294180766685955730, + 9238358092800253965, + 7709116676295602642, + 14916413501010004749, + 14279538316854813762, + 6492189398191727253, + 15844436836446155438, + 14954552380306279387, + 10080919454759758277, + 4687874855108881957, + 7920082235919198799, + 8506515029268341862, + 10661675097046054645, + 11384791627245064188, + 4016375462994977363, + 9098406256846847171, + 8781586080093561168, + 10296945054534352046, + 2666528116229498946, + 13263345244175763051, + 8907575691728723778, + 14233496608767174209, + 16847385849046312325, + 13405122157987209580, + 13979436435588559576, + 11761975213098607172, + 8599320344672849381, + 2439995262352621168, + 7297795979055740389, + 1816748981987548904, + 13837471676312594333 + ], + { + "siblings": [ + "12839316925570005494095391447327229980614787845697561301930259230809125893140", + "13213468880797852930766493249967143715495998030832820446706708828520807860818", + "12431959029301293509982317361426747647757311597796698964245284447647099139780", + "4813106548026771244532208314835335653068657993190551140113263218458996060394", + "6742035660423411497524576726044881682809819937704000866843146113206270468951", + "18863489449385602602790652989097763575565720685078423282307698838753804900320", + "16662810806156789561612933217347755000045572935717270865098721321578581105821", + "15775622657419483002725706553510136482846597874608164523735269412293936881253", + "5644549005389408898146293997310181842039854948202675832052908273812124901909", + "9882038014641472212646939902938344064965154357107505169555895358104958566420", + "15548996507254871323936991587783305018325291618358822088650288020795704693664", + "3052389063881961436540442321815848339823607997419400655584187900535068367166" + ] + } + ], + [ + [ + 11996788938767838952, + 8006886190295616550, + 3128095315313972072, + 12018064429598452263, + 18342735393230189523, + 7869543133501323894, + 11162817031546908257, + 14141001592953149146, + 8556024867210945415, + 13085260757505778680, + 10603005396827187866, + 15311221533571293274, + 13153476611921626385, + 17443278029815365108, + 2070572874420129844, + 2693950796497674969, + 4082706719145171859, + 18332653585636881937, + 12532569365087448796, + 12206761162644913453, + 7886719302126561877, + 13144792602560789990, + 16391118030405903210, + 15974753528775289440, + 11139501124964919373, + 14193718910308884682, + 9821239514058748342, + 15372553919428183354, + 15426229933672160647, + 13239389228501021145, + 9227649966647071129, + 4120610033105483221, + 13237456586789422028, + 16240073946223524731, + 17947910492537594954, + 16246364487577880552, + 15165301089881587713, + 12919420011618657495, + 17916237167782961973, + 8068809778433979750, + 6036481294213140887, + 7607172318426454806, + 15869408662230894359, + 14982167838406647067, + 17817435472419379111, + 15498109394962187958, + 215100618113691795, + 11631209246138874687, + 13860595934623290426, + 812421217253074133, + 18057063356730306065, + 12793505171483559880, + 3796941873650353959, + 11456747489843671838, + 7344062153085453430, + 15578401271199288995, + 10880777989971385153, + 16316267273194324236, + 14256746968730656174, + 18423108928069023672, + 3480957738405646181, + 14904674946345136403, + 10818378424877620180, + 14381135538886881642, + 18261143427467885473, + 1754602357246779593, + 16309797096072624477, + 14950224493265356680, + 14532860740429835889, + 15733207499941472204, + 3153786743598698366, + 2611168248970475892, + 1665820786011166332, + 4818990204915158948, + 14623310164437422105, + 12291049387368492681, + 3856625591901752900, + 1543783313196205430, + 326073332227379930, + 13881256106452312216, + 14099830627141338150, + 8835874648474160874, + 17286465851738185085, + 13976076690889462478, + 2044621328430171259, + 4309243602426296283, + 14763231311922447711, + 6853884555976405196, + 1950968112647843204, + 11269623555408120679, + 10754671527697794868, + 14367907374611287001, + 16386259877916797335, + 16620652635176345079, + 3552835369648936119, + 9695106102709337335, + 7086032835271513268, + 17472001065929406704, + 3608067821604146149, + 3069067160732274285, + 6094762011791679811, + 16185775756792256744, + 5558831233070965617, + 10424615898801293470, + 2670352483731877295, + 12489234230851106197, + 1669035336525409762, + 8396973705595079309, + 15989131588003087045, + 316971146802389979, + 16096094412050995409, + 12628412747958287810, + 8813218119102076294, + 8059777615799225385, + 4484685297439974486, + 15015860908447915682, + 17531000324576872682, + 1545079526561142231, + 12134184680238089523, + 10075309349218196872, + 13809606640159313358, + 1620671349910736570, + 7870618376422361272, + 1118820306570317142, + 3378371823645260943, + 12306039497934186353, + 14945760833330988817, + 12887187564095824670, + 15970431702706212242, + 2098578788075230381, + 100179726588058658, + 18096250855986356339, + 7299140703401039331, + 3592050707151517039, + 13928363252333760875, + 15186425376489029596 + ], + { + "siblings": [ + "17188398412082590678785751297169139799785057919993098945192031865544214404690", + "16124005712720629568175966354561758077878089269634156138912327972745110994389", + "21157792975996025000339898373022762735775005012048902112351173600203568752105", + "7744367664516358614731146332926954364222230861525754155073828545783646557394", + "9011598469375418426390606150185862656747086750641879993916499356198097132092", + "18170612245571638948751349951520810561825895772603558806529860032005785973416", + "8987800403506793522810837801672622637886622085130581595591265773667683878275", + "17463646737453675147877931095526737722275797445292567018897657370773996346100", + "6473208384259277427881239275193648571537562401507370749182347999637154150314", + "10291272890207619225022157839068967934321829529422772281982091563827005149286", + "1134279433659963479054279935832187011417237195376709990164718285871726019313", + "19907647880229553180458063355832292580704725880150563757593183472987031111254" + ] + } + ], + [ + [ + 18348518865276092752, + 14855819304269554680, + 16144567436803539702, + 17415418513989431575, + 1792368832678139405, + 14989774673347121384, + 3522883202108618328, + 2425044065908158900, + 14056095554249527083, + 6302908435037473101, + 9409491457827702313, + 224417224861469278, + 13125960165462973978, + 6344999268045296690, + 5065194806773737000, + 13246235610629873440, + 12226705873631951497, + 17826222569723739813, + 5189305332070590115, + 8841453815370538709 + ], + { + "siblings": [ + "11580330770844220666828132086524506141026221853032249879481754915428434280031", + "7418685002806746366273641348582281398333264542508488327685942010260232554551", + "13930146100630025587891895775601251907629555600949161330490902576340020800136", + "1904428734353990364650229057175701659060380187682352646663476372620191283058", + "17021147670299426846478101695964072147725959023327109396941920787091319498599", + "11600738362934793014510936891620147754044508963537020780632664593078689472920", + "20008599594694297621449233704929701869054671958718500780014957522991463090449", + "6433341277340954729429729023117653532989232450978277794129314648191549389874", + "12017402897533794734297885030527530325522694641271378534250407603727347596773", + "8670414237874449638500075182867944235634062111981837577277380528769086930613", + "15318466824707100993110386514039688936514764028772659696012539443954136688148", + "3558585872779213669309737306952931928333178068232712760299704133667436697122" + ] + } + ], + [ + [ + 3157907650175046252, + 6551186616516253087, + 9255703715414095621, + 17041090027732328238, + 9773183954764628991, + 9964425319460189120, + 16742113276191753814, + 15720606821057558178, + 18277543048852173662, + 8770267597778633528, + 15846655929948858933, + 195554625401281123, + 5647482477748094739, + 7519889881209191841, + 13556532602886998773, + 15687761440752542677 + ], + { + "siblings": [ + "12578027199189493955033262330917811587677602626571170215257035319287209540292", + "17190343872186095613348423317895550522168692059406653045428169438395438614193", + "13767550309183094470891453914393287070330280724345921269027652479697137154098", + "7970567854662954637015234596800236362502499468145098966068141295610039795407", + "10947898072875151009520598582265124401280157328537724143629789845735986279068", + "16166260510045219127214479698764533182641869772967830639802600819004752266600", + "3560988677094819325814465867888763751078674259237957004836408169582614800039", + "15116153000663348468442645994895674833635596579628540608876684371577015941160", + "3119392081262866200769143157371385949918996456518649461739490588044007311508", + "6941021872319985605982227118819138868885326815518400844113038486937967319753", + "8856904178701854803101082739084867781834532557176261413922227160904759106983", + "8460210815005422617352224613560580100881430298936063407451580524578463703358" + ] + } + ] + ] + }, + "steps": [ + { + "evals": [ + [ + 145291875775783013, + 15711973052636580678 + ], + [ + 3818582438244111233, + 12230702123329419347 + ], + [ + 681401361316764886, + 8820049952979228040 + ], + [ + 844454873702878475, + 4509648134940965581 + ], + [ + 16362439953409256122, + 8136575483487053884 + ], + [ + 12140729075187181890, + 2694167392625683468 + ], + [ + 3331692645359302481, + 9563425597365791045 + ], + [ + 832210097169607416, + 632938628515762913 + ], + [ + 13094641666537187826, + 15317886898416506606 + ], + [ + 11888274809568439478, + 15873134304305990582 + ], + [ + 12644096372974719149, + 3835050251706685535 + ], + [ + 11551007921604495656, + 12832306053970667769 + ], + [ + 7045892068387683580, + 15550991480707912708 + ], + [ + 17600749199002835100, + 1671146448717686822 + ], + [ + 13840577435041307840, + 8385262477705143996 + ], + [ + 8663708153679477003, + 4236217253745665875 + ] + ], + "merkle_proof": { + "siblings": [ + "10958281089714517354620359938815365632298332421550194011377860308683394207097", + "17983888140609917438555667143756887122237008116219649547714313275021517291754", + "11231873905400769633013322018429408222302123956457848161830752904792106150813", + "600659191485413645097912148334151526065028852972828894147824291519998322885", + "16884150578304455626320633792589349280441403053847769741069427031990314612318", + "7509408190349266762868966578264090527325249392092872030234268220892777393722", + "11684310152033714485194275803980489739969515137145711811046690824473940986337", + "1386464104167715077529067685264353096493867086595897860471132426790276041540" + ] + } + }, + { + "evals": [ + [ + 1101851029086076919, + 4430353114806625577 + ], + [ + 1101973512364143132, + 5492690038737917294 + ], + [ + 13087829459667565548, + 11185412182511997914 + ], + [ + 4470271205605381258, + 16216977803354836686 + ], + [ + 11802384639720059203, + 4450551250509706143 + ], + [ + 1937275528638224499, + 16532047285221759177 + ], + [ + 248621176060124469, + 11766679290062784084 + ], + [ + 17010209064918955425, + 11461828177604440433 + ], + [ + 16176250445039264404, + 3988836470993496919 + ], + [ + 15004598290401980866, + 710005158511806788 + ], + [ + 12897108174757018066, + 16868507592635361072 + ], + [ + 5371149308335782936, + 17918289009775238660 + ], + [ + 10977735885682954059, + 15660809806961224557 + ], + [ + 3572618211143453649, + 5308583636796881385 + ], + [ + 3374496725524935688, + 9203845991426064067 + ], + [ + 7076768319229063043, + 15299379114461645769 + ] + ], + "merkle_proof": { + "siblings": [ + "11705576757916966951217803634560837844426152751342125120287292169683434567010", + "3581322833504474469247731881311113342949193769072446271302155573166609553635", + "9052259441371016998472041330186733007801431716802020974058723817276563489362", + "4583047607711153260708918358925441022206255979939554413421385732789286686201" + ] + } + } + ] + }, + { + "initial_trees_proof": { + "evals_proofs": [ + [ + [ + 12646147221271623588, + 17961844240245815019, + 11029695725347596650, + 11344917242964177615, + 11074261201717877749, + 6056697606342504387, + 15938578482597733508, + 7152825129975931046, + 9385624706769942380, + 10961655215212205134, + 6128962576047854650, + 7277058056485281301, + 13713428104273064053, + 573074995161512377, + 11407883480541698043, + 9510344536638980778, + 16311186261627378936, + 18090551410151103372, + 3057283431493565120, + 13438520501567390770, + 433508563244375141, + 17286116186287314023, + 2703138629746621866, + 17051627340269391259, + 8010596218744218769, + 12770310912044028592, + 2028692325170567636, + 968111266798154027, + 5408930705581845568, + 17937484572520175352, + 14590080062986231417, + 15806023849290694076, + 14747149800026680076, + 10265097444040791861, + 6445833500440337220, + 17414561721766686715, + 6664531245750977275, + 4545652076230543277, + 13359854156039188265, + 5869841922497202277, + 16860209641293132506, + 1074493886086199970, + 4530056958447600306, + 7442098235995632634, + 1451389988861545624, + 3673804881210581864, + 5075746215250889532, + 8641849187203099023, + 1123699391027639142, + 14969886657717823782, + 1848436647346175805, + 17763790578599314150, + 481353890185751230, + 3722978047414314847, + 5165812341211334469, + 4748012912599611286, + 10602763472795686900, + 16638951155230116752, + 10742430881687561513, + 2864689148922194731, + 13035054095945763290, + 16949326871040996717, + 9461240360878237382, + 10058671211199880153, + 18326219688158980844, + 13118521473500508098, + 13701551139404656116, + 15343784457522212747, + 1932041797734488030, + 3732899142573515967, + 16245976093484076754, + 5984405482368000297, + 9583794291290631920, + 14666593077671765025, + 11216058670320343309, + 7871477458115986357, + 2518667215110310490, + 9892954537581467682, + 11889776434171064909, + 11664429882056505064, + 4804135851335190741, + 15634112051443235363, + 10022130331748556617, + 5416855217072972453, + 2624587873659141594, + 4839817802327789871 + ], + { + "siblings": [ + "12565965166558922274386237993466306951683733080770714556970416726556766662412", + "16358816355942150710513195663331864536006123106221153415634769991998954465342", + "19205959868865680611814290039789616027304691299549877503229546779989600812871", + "13655849073733435298693212794897855276363639813364754941770434610594833147431", + "5477045533290302377110976950283111725197321020833269525983070425278892601588", + "15141408384019370534691729600809369929504142910102020452136345628963587182408", + "4263157573741476632514589194070191037265521872515896434376088859479258051865", + "7824432532384967530007024449098550748008755404732103678063185389754215270451", + "8125357415852245237369751777689742037727855014703290142996428441948175799054", + "21547132672372259570157940316034551480407415505555441912092613219810251411638", + "2610251703461833281523386351679066827884772218791023479102261046061370256844", + "9888001292999716420031032797485093767701908984640927369602334231136590693908" + ] + } + ], + [ + [ + 7316113633196324571, + 16272989587415087880, + 15887188139377046433, + 8331354214916464943, + 15524759622301744076, + 13197434256145629981, + 11180153869642524891, + 11169942444889559405, + 7649851641323995302, + 9968070219692818801, + 4912385828957330918, + 10268791620233832173, + 1365182149822197525, + 17158850315439955870, + 1555330204925588350, + 10420696491855623648, + 17747622023639141250, + 17618349441294825784, + 2403638566927933723, + 9433621299870872055, + 1897695064738573727, + 2255569625662311769, + 4138141081025921965, + 4325270156561501568, + 3728091082021572025, + 5908873600806836611, + 10639769605744461309, + 15700196488627809369, + 16062394104347701985, + 6245258184813423414, + 1295203892029713895, + 12673030685483325332, + 9111945410535072303, + 3861512033742176875, + 5768586895639383822, + 13263619328661517344, + 15198554273936785668, + 11132768081057856448, + 9272117895061021704, + 16348828352862211759, + 11158962687720628943, + 6505464173264946268, + 12454940670187577685, + 1445902172766892543, + 17743711241110010299, + 5270085355923758110, + 18252254283660453132, + 3742067106950544233, + 14212191658322746172, + 15069390076087552168, + 9492675981990544758, + 2387332760772346317, + 2040802011926209088, + 11503215924935551321, + 3113876429411795059, + 14939068314388961014, + 2311790003348562154, + 14688011265256793121, + 11047600644875456642, + 10610583844019390720, + 4513142204838405171, + 11318680140177951047, + 10395676928149434950, + 3149768324354927913, + 11703579491685824579, + 2645389417492441483, + 162051407451476063, + 569811576762053254, + 15008661021709596589, + 15049208721364016515, + 16905979119233274619, + 15682572477271149380, + 7240615940293191735, + 16954530992983834703, + 14697336764569056297, + 16248325902306622614, + 16671582332315097390, + 16338366268142551636, + 1331685723624070848, + 14654025385346596421, + 1429906677611896753, + 13799895397238876291, + 10208123820853043096, + 3758425958820182918, + 11940987921878478100, + 2179403241307401962, + 16887388289287961397, + 1527411344552623147, + 680874587213042350, + 4475555205048443797, + 3196849221065517000, + 5056431750996865266, + 6229507327980764813, + 4109599162640887622, + 11180929913695637208, + 14221625699869122159, + 10064816673410047550, + 15520708166368206655, + 17602281124147101206, + 13195945557366795625, + 15541847542788568045, + 17120126231050144318, + 6506492382357113582, + 4732008443339530584, + 13444421738091064331, + 1587949213029457308, + 9010286274689010735, + 13415768846924277893, + 1934873873999550303, + 16097450605619618022, + 15405147411814892449, + 5817834961707818023, + 13822528483760686649, + 4628274063290174502, + 11413994060580565816, + 10712222574866375621, + 16946896452700181089, + 9119901794952787219, + 783697505373857310, + 1397010711402865285, + 13647400504823679314, + 4137868498337971612, + 16351990472563697804, + 16352459009905987732, + 8402321887870478329, + 13511163220577938118, + 7249016793529539075, + 16133167814578733806, + 8637912751664898153, + 17530552084245125586, + 9428060262260605722, + 13147279554914376766, + 3427692116322799980, + 8635324927135043968, + 9632635916332133242, + 12361074012213132164 + ], + { + "siblings": [ + "12493298208649094219291858919868731731536035185913992008800102770014660720000", + "13568693711090741046755529767165372777499195768461813386466393609612169531042", + "1095392106094221831090335671489762034883680556891675693029373853186345904585", + "623415801194758498244620041812012262991296009545839710254964497266575633699", + "4444684719478101669297270462001724899428181268467164906045623064061517157170", + "18793850317549227968433788582211841782445614329231994094228175656847104664943", + "10100280984613232760622752568330786329530915180301338781824429926859873987548", + "9569045710715619006901391987708821318785045999615971107312976878561519035180", + "17929846600717946889812963643657495729956501304623450323722744793171253533415", + "2947066544149864463643418837317993475203702758166926408879033223520142466653", + "11936858854077771413993875451133274638317902740439466501065506460247316804023", + "14539885376542550175378100483810910943446933596865731427354703979178215630950" + ] + } + ], + [ + [ + 11751216530978899494, + 7907126166069732846, + 8216215133252406944, + 5760573003391273111, + 8186877801531719338, + 16293081382553125361, + 4123406811595924633, + 7708540675445042569, + 6150426124058057225, + 2292841705018526589, + 14690038115772615229, + 15432284480120229004, + 325433559425092672, + 16983727994386605025, + 11497768425569863256, + 15055432644782954332, + 2006231489415320451, + 488800997356079109, + 17750677114031789800, + 3338288823856257170 + ], + { + "siblings": [ + "9492154986521996164841735413349950371773983725744435781557000124185713933121", + "20342470574195314496424813307927054888698069110394838947260209734158642830106", + "13935560785337669965470152967589500689448591909257197957713368144153646690105", + "19660563770933682646111374479748432356681188524066624858797497994167226662522", + "13931004144428522840437308744649082909180088557521637149825305697489406076278", + "1113484075355415033841525364010857218109667500445300721489768297407323390600", + "14960006876625268669166134757074967459177524962315366449218305027969094272385", + "11998236165184402076563912715572977528597430823618408930990840331888269075692", + "7883419689036515920641792222072889290675793119647084320477645954469412981303", + "20260919741819512003662309724079080563334639576733705579850895360980366940106", + "5706802425855489831106310389243192949807004039843661432670563698756829554560", + "7005358500874429238095316086292316313219511845922250372416547988560313284452" + ] + } + ], + [ + [ + 4913639109805872812, + 5028198753860360110, + 16796801576523114747, + 1058549156842516797, + 16506776248271953968, + 10531040528368699682, + 16156456735257779359, + 11150245909512272054, + 12359272651893264824, + 17246124269686679888, + 7251743043036977613, + 8597424186174097272, + 7689454184907570142, + 1123235222977651501, + 6576332101712442531, + 10661699034596086633 + ], + { + "siblings": [ + "5782941330319908547770891364750896754811620906441783812580390784048416580189", + "180146924130615255910561158806951706407397589673342715160792404343709967895", + "2934069735928493306707715189049212852848822799091274329866820197129145412232", + "19310234462999697455545302395975779453824796517270270696355934838523571515351", + "19225793079232550242377784170561128977172578188995774268423580163319533645144", + "7254411482689926933056214068067518656638118700321705654614960087393301893938", + "7759082207996136692084193514366622181420747120377828399572749103897109078461", + "2545929491568582475895988107066278683319222823678426410149701516546520483041", + "19591817068291443962666969143481267554031359069954036508888975878368095586167", + "12962917710917386810493956616418185707874662732168749604856497173102467507348", + "10938381414370293443171474261715944144525595047588741376719268277838239826973", + "8961163928825942000671333894516467224519453609004039352602359294448829188179" + ] + } + ] + ] + }, + "steps": [ + { + "evals": [ + [ + 821637132979186855, + 6187931573745694120 + ], + [ + 17895372828434653242, + 13244094866433602902 + ], + [ + 15302004961876959704, + 9692224012686865106 + ], + [ + 12172676696599495610, + 4515528524223509139 + ], + [ + 12511986691493711221, + 16601774488810491044 + ], + [ + 7519222646625662394, + 14021137631295284996 + ], + [ + 3572361038840400319, + 7559402826396067028 + ], + [ + 16219983168253302676, + 5898636592271113118 + ], + [ + 9667939617650048464, + 16311796935651602663 + ], + [ + 8282901911046361848, + 7569679876829133223 + ], + [ + 1135179108683348219, + 7706066169901658011 + ], + [ + 8043528126990067402, + 1994018668454827670 + ], + [ + 5277905317171435305, + 12477823338908684961 + ], + [ + 13655454439185366406, + 5019081332013319981 + ], + [ + 131728996440081779, + 2596838177215469648 + ], + [ + 9966875950942341506, + 10765147371317326967 + ] + ], + "merkle_proof": { + "siblings": [ + "12133567375042495096318598768949215201785295323693601674242994304139068578890", + "3939052259008434736858875447569130236738141279703985544732681461664099954751", + "11842210686305691216494701301922559067305366071063413148634728236486125362770", + "5516152820513306599186568821105847223239050157217692493554457605433876582251", + "3268837792822057599036179948562060498270930688274422098095964983776172205525", + "4935999662296705782511806773328205076143604632222812060408611636520991860382", + "527802535165998419110321730550746035926256102729075437882904434439793962012", + "9764262045267084452573658547521284729605527919872417326064635513794641869425" + ] + } + }, + { + "evals": [ + [ + 255230110181225607, + 973554596899177641 + ], + [ + 14741971148394377832, + 15814611466143762539 + ], + [ + 14507115807838948556, + 809011499583834491 + ], + [ + 4952573111269396507, + 13491384288631652864 + ], + [ + 11330651520825926328, + 16777944728681595175 + ], + [ + 1867798596598373475, + 2305133616839152939 + ], + [ + 8036376775526197872, + 9338089378514396259 + ], + [ + 13409468139538602476, + 11084865033562118640 + ], + [ + 11876246025773384757, + 2171060287448847187 + ], + [ + 1797774271845662975, + 16617527788064792662 + ], + [ + 5463805415736306430, + 6171417903387167929 + ], + [ + 4755455324576774985, + 8009544082780759333 + ], + [ + 18324821445570273826, + 9484009171610519493 + ], + [ + 5886659728160291129, + 16262219193436083386 + ], + [ + 6314296392769474930, + 15301111622673004733 + ], + [ + 15767582322577217102, + 3943905471896519488 + ] + ], + "merkle_proof": { + "siblings": [ + "16119691018273188910126752438457655587792953556522474082167006409939865063754", + "1689971780018340063848044299398713946072014008728004175673320879098579123830", + "16250710437654781795477055260628147069873501263611023846238048066187465301605", + "15574248526700924832125412373859822631566279772643807937967018867441721442662" + ] + } + } + ] + }, + { + "initial_trees_proof": { + "evals_proofs": [ + [ + [ + 16051557980335983394, + 2651719737289498738, + 12795118483192558666, + 16070711954224043941, + 9913887476367534046, + 13896897529834655481, + 2240680580526949303, + 15822195470320258945, + 12814463021209079038, + 16543432607957012695, + 9031623442907881395, + 14337682158343242149, + 13910280896456149605, + 3090050244803593872, + 14206315224372421925, + 8447524260658019579, + 183212845532897089, + 7033484178466428962, + 3532247924060425746, + 11623554268336311927, + 3334062993441752732, + 7096006235266281304, + 16208123926494270140, + 7193603093949894582, + 2472851498775504431, + 17399000527510808156, + 2634204035601561346, + 4035405716400999942, + 16069412730657650781, + 5260279655956104704, + 7621847405283398889, + 7649209021514851913, + 12046130875880439729, + 572632828246809254, + 8758668208421552012, + 7384517025228769268, + 8094675615091242242, + 298887648136650668, + 14857292048787449736, + 4015304625801899964, + 7391896939995212914, + 3878658945012341077, + 11098641150046489535, + 1783682401535578216, + 5059898303318121793, + 18446229524880269472, + 13618120611658802633, + 12607769559890619264, + 5429104096893222735, + 13293151842421615251, + 1170580840913338535, + 2120173876789742063, + 15800850450460006466, + 13953837632573512598, + 3143972398141836955, + 15610844774643434119, + 10789812178723673392, + 13269250220771723976, + 11703254272615855988, + 4683390099291541603, + 3421245253401268573, + 17787875688720796286, + 12279697451883213233, + 9936444498446981084, + 16686181315948736044, + 11578568459356575655, + 12628961141409043818, + 7541538360846954826, + 16240295866931722509, + 13694579047589247503, + 3955580805602734023, + 12281059374366744279, + 9175245358862426111, + 13882229511913873539, + 4396658699593496425, + 4545825587336269831, + 10121660913359314235, + 7244626971996552557, + 283016435347839311, + 5809600808373034406, + 439617280602079931, + 2201036221584251953, + 10869492863777545160, + 15814895957696191543, + 6621620706999863833, + 9135641766276654993 + ], + { + "siblings": [ + "15971493793942479357958220722164633733999275197338821849441564464393635891556", + "1383918953271659108497462843926453523567714634723311816919545909410355159528", + "3793257998260514591880891362800819871219928316254680990695097577868256005732", + "15325703495050974222107389063841525795507625241970179510158291944152447380603", + "3770736964039412120874407032516281119677497794372075654537166049547318111364", + "1032248069692212667069927880003058637705721527539962727688636566569686504378", + "20737772295261642939468978243116087331279260861532005377754152767454466633984", + "2402021211454906935615026743078849914144011212140380325429656191291134870399", + "6225893656015144523982583995676406797947262280131907953132957608351933303824", + "16132334943416660569973226039785752340829594917811155114923607348995403507512", + "1822664253471450096674096541121402521978814067775000024874314924058640030721", + "5204520435214027488967405792202934657336058379836924015238788787807213882509" + ] + } + ], + [ + [ + 2033859860037845935, + 15508669003538860184, + 3771332202602770430, + 16186587405037410222, + 9926717645011986567, + 5136303615025173575, + 8915932921176454159, + 5993271596407049950, + 13722279602402196319, + 18313963541519715487, + 16217319712349775030, + 12480246387076953698, + 16653010006963721906, + 8243164851865205434, + 5788067491967326126, + 16702909491417671666, + 14469072435190048823, + 13699007823557831894, + 7471405063875201952, + 1739196050926821495, + 14237599170387047583, + 5542541940715036027, + 4103725228768514103, + 3706540353844314373, + 8171728891571478173, + 875689394776391931, + 3379390141680057396, + 434519923079021102, + 3953075347183746934, + 9229880024608576480, + 11239369055657175245, + 967842542234203789, + 3349627658688331791, + 9423389119075330117, + 9379414437298586451, + 15015858917323365286, + 427782289709530904, + 16310569429263514564, + 4460388326206711307, + 11726077100951968095, + 768109766552581945, + 17760359184168371680, + 689285919704067013, + 1546108188673226489, + 8829450066178559063, + 5841040402245690467, + 3817515117185904449, + 965517507247443435, + 16383620383882349307, + 8380713120422887046, + 718445637494670000, + 16623921021364031115, + 9720807516741554534, + 11194171088551087136, + 9821396459918729495, + 8651984679916485727, + 2813705199311819652, + 12033216146824080319, + 17767010729014186747, + 4795093937075047574, + 519031159949719650, + 11903300730953855720, + 3350710751970408991, + 17482207612845825803, + 11960818975322305661, + 11950666384225924346, + 6142239737886077347, + 6844116590891144613, + 4270662772709382126, + 14544100725102722008, + 1554592270532181560, + 16080989434488348386, + 1316893225383441844, + 2284553599544985877, + 782134660100854035, + 11046730724113218990, + 10970656128602231621, + 1545682668063233241, + 8097824288937485820, + 14446307918716163282, + 5099165480614299834, + 279528696024595968, + 12940947408360330398, + 17625072257904696782, + 14773187867777684671, + 9018560728371054015, + 10558228787545392108, + 2763496949916359513, + 16440165084676287810, + 7881324087321198379, + 17309741085754346403, + 1721763649246302271, + 9597461768049810649, + 10231201319715156859, + 1428873881730080425, + 1905596140354353472, + 7147251998123086462, + 4176925889653940218, + 9744270237352975040, + 17714892483930917937, + 2253749046567177207, + 222908929986067258, + 2976739836318932547, + 14678042566275173597, + 2303280482188735091, + 453637257072125682, + 11937002443755176308, + 2849765707919578986, + 9672681461343666402, + 17197618249679867355, + 8108401252212168900, + 16991849471742544280, + 17391919139277267449, + 3187899986261143299, + 2207893524859997722, + 9371940361359870466, + 17238187195563682781, + 6762700317666090873, + 5233380452404243069, + 1872294196059325652, + 4152153663661386822, + 12669158007022612406, + 10599474651729347358, + 5636828285393456788, + 11641461364483998482, + 16920456653304729117, + 6601185012979168352, + 16071733098184447970, + 8226658581660038990, + 14896434005303674374, + 1546887988541855572, + 17750948618846454153, + 5648581747582666156, + 14728427116753083155, + 10184995151056762985, + 10086112700206607463 + ], + { + "siblings": [ + "19716119253498476098295531975711908326853171941319464229401793302532846169547", + "13513393229909516947356636669756245105230896788511899038161208381875238618347", + "1905168834978715616697314938830456841934746811424707698160723045662078952939", + "19099010997142170731103666775831483233174881887121667316286727211651483926156", + "6667934509169419214107863439514626536072350733000021899156855573938289564696", + "3716007812869672506972186652293052465142118572076657332436608525517365389225", + "4455524312189346378174695845385564673664157041211012486436322734673143578228", + "1640241222909126795278732674458850609036367484847785934976237828731106807333", + "14483378192347594716867183309136632116616843262665865177636786345336340643475", + "6877063460380547391115451815374297664272565218462893539505047633873817607741", + "5639619007967409599135528151607692195019520121344441642954101236908598848887", + "11835395864385423637754169914981742464874748641363926247693304566719865473762" + ] + } + ], + [ + [ + 921310441183584338, + 4619276417797186836, + 5128136113297237107, + 11056547073186388984, + 11644078766152099106, + 2604516784050179643, + 8169741626433416317, + 934769270018777755, + 4803692136297508704, + 5739861851940319396, + 7481620913182652096, + 6666784490255094665, + 13899580851361507015, + 5411822473319180474, + 18263794967662683953, + 1171849231522272858, + 6367167105658081123, + 6104118070913556961, + 12642030273443646653, + 9871368148784431488 + ], + { + "siblings": [ + "21226352360316330128953838812299551660884512673610270968598067567022123346030", + "16731630872472545102947221481215666334065911498830776122300618225791903257210", + "21304719830404537432318929150790135113602143755814189964585104842947642494883", + "7888990950585893204714973040891577888167573240635850759967325187668395326264", + "7086005397514386481817538680294094546061764879837431526457211011861349788838", + "662753422775201055193908421840894564856880010356030389969878958626444730914", + "11142350191265883148255857099056725438342575809320810287826934419844244389211", + "4453123900418443879996911015605775827691061096238976721443735235165286727318", + "8860104374423609850694135977899804672346176711931147946056883145239163281127", + "12185212697178488748767238200841178265000261371556329854814328912271035410503", + "12592822112999626094121085145145072049671055711229194188680459233345677353485", + "7270839071145803213801160862352709488574149998127565949010260291260883109988" + ] + } + ], + [ + [ + 2087104059673150675, + 17107390402490310342, + 3841253698980736744, + 8142482361411400759, + 15582474557730611251, + 3529628697149470690, + 6197962200479222186, + 11158797404303693219, + 17305232945814960385, + 11565476530811931420, + 3375135732541845453, + 5804001985408406025, + 7063379484632270390, + 6497648305765781501, + 11952969406908224466, + 3625470223320040071 + ], + { + "siblings": [ + "6219085268327068718337848024918729030077756624409958688764823759578094289240", + "19806324072806910273533435481405137026681446308871708336105250830081094170857", + "16256721265141010625384440537137083776945613668269033168625732912212374905946", + "3699300772967062037528540585806400372280395525496637325059131550614104168448", + "2274076450879516650903464885443108075993112534384610970153172211556052858027", + "9053305990166968633670221700612157781455266335846809600616292586139278672664", + "964650798727140458108342907798510465344421386967628334283581822041569884905", + "5431358681970856060261232328694168889979570889264695935040551692205905652960", + "11097620026438070646653312896615054252511393456574174986157726595586224161075", + "7191312506765064057151485469950044652943219900973491886698885302765016353134", + "6468421867870370875857003826217504280500565538733253012637748192342591360444", + "15026442460425541478196815128473416645603801794641455913264241149249949729015" + ] + } + ] + ] + }, + "steps": [ + { + "evals": [ + [ + 3501026021271048195, + 4681034410781594784 + ], + [ + 453510683294259967, + 7645749360010012500 + ], + [ + 15176213641787948149, + 7442577160388338940 + ], + [ + 1650913270474570739, + 12208535847876993719 + ], + [ + 8970013949813170878, + 380078477723220164 + ], + [ + 4369576025318818265, + 10340777141575750956 + ], + [ + 15687204889819670623, + 12104453372084499609 + ], + [ + 10729426219157326439, + 1172162104432904624 + ], + [ + 1857243858808226795, + 15410218181333001591 + ], + [ + 4726689940557149417, + 3798392831394623109 + ], + [ + 14337636253634849242, + 9282901846636139934 + ], + [ + 6827466158051410371, + 14973700591287762889 + ], + [ + 16106530558027772906, + 9050827022835748789 + ], + [ + 15841396641820656841, + 12902193894436367136 + ], + [ + 6131463653677165640, + 3419253731296715090 + ], + [ + 1436093588999505338, + 11304480665362288142 + ] + ], + "merkle_proof": { + "siblings": [ + "883121738343544745408665357708472692724221254770051513686284429956454581600", + "3586392879519906543969565030252345342670016792120438697214152331635065241289", + "2473421973294465915173983929029429120832794274250969692846456359510264276750", + "19882480997830397388976889787693587431525557461416602685106324678742603782622", + "2240580530007781600468588788774332160163750025258597802077787429557844698390", + "19667889326768177104934486245657223965185720057509613951107575138028844487251", + "1646840622173485055693875367173830140120642207388597177196415291911066461497", + "529963510332887629991608018729123103986036198143669189079282843665950520358" + ] + } + }, + { + "evals": [ + [ + 4316831806875625121, + 1750703808272148099 + ], + [ + 13131658575510042383, + 7796606113072408061 + ], + [ + 16804016699172450192, + 14999395110205656012 + ], + [ + 8243719909733079975, + 15858412528067953134 + ], + [ + 8823501780635388053, + 2760623185379463534 + ], + [ + 8041553676203967303, + 7721133806424823846 + ], + [ + 4795168388755809846, + 9448366762343738825 + ], + [ + 7502602188182496029, + 4143507240478790689 + ], + [ + 8566094081772126708, + 1207350569920377378 + ], + [ + 8207458160251909636, + 11635492800198596998 + ], + [ + 4434226692460733082, + 944263232735169821 + ], + [ + 6605867191242044262, + 235364200525056210 + ], + [ + 7852771170742518058, + 738105402543383114 + ], + [ + 3699169067469390465, + 14533033358697409319 + ], + [ + 2920497091856656592, + 13946597491052862859 + ], + [ + 11778832752700573699, + 2960954875969679504 + ] + ], + "merkle_proof": { + "siblings": [ + "4424020468095188063832376722471733004770184892395110704286419649957471409503", + "5741094764911314267786133548430683345672403100376097754679526198980741651631", + "8077458128916972907733963117736545413938075073590884822058122057597508032390", + "19235369797274353550315397400424162762565252539997318237178991694005902766470" + ] + } + } + ] + }, + { + "initial_trees_proof": { + "evals_proofs": [ + [ + [ + 17398261233230046331, + 15863231305676109221, + 2723841374767688373, + 11428275562506743546, + 16620251138741957269, + 3938188597360289322, + 12393818289732839906, + 6984619983795243513, + 7764520087658586005, + 11967994698697740310, + 15886895494546144270, + 14632728858199751096, + 16029667511660978957, + 16358957475801362788, + 18130879118672580100, + 10392280378261301728, + 16263135211674382308, + 9208177641675350817, + 12673398045504549436, + 2509536932649253848, + 746852266704579236, + 9044704403531153278, + 3338666984398610577, + 8705802431976230496, + 17755578500588474821, + 15384438792451814859, + 13715068728662767036, + 6641869544110034740, + 1193374159042001793, + 6263653435435085444, + 5896920876236031787, + 15188287185329707146, + 12275412250871939732, + 3095608809410162146, + 5230013037541377157, + 14379546826146640043, + 18349691978428448519, + 8828889472562316673, + 5430433038098891463, + 3531504236219656139, + 6559217885218972260, + 4178082706165075988, + 9293943262664765920, + 1306632015381416403, + 9216923381041571439, + 1895583889808878222, + 5057111683418924444, + 15159811298821804854, + 1008514200790664737, + 10161351494870643101, + 13465041443556134876, + 9320283948521561896, + 3500266320937426938, + 6983510226246389689, + 7577758690996300313, + 903764528766927015, + 1592903263882429733, + 16531609790870523116, + 4119921040535934531, + 6635012237156991616, + 14373849704233229263, + 10574216546166033640, + 10411969029143306722, + 14855016268008221837, + 3606256873694532150, + 110098222442602955, + 17155032365562441368, + 8065138949890202573, + 7347124770510004462, + 7143897867008411782, + 3276700306055245391, + 13246579918684797134, + 2543594067866329477, + 9762842862212918529, + 13079213089359762785, + 11542854922710481469, + 6741346173477814691, + 6897467669207006654, + 16656586293432438885, + 6957296941163621650, + 15934583446164235845, + 2734419971949886424, + 232125367402702093, + 6350383644818161991, + 13975450354907149346, + 3900607781345514673 + ], + { + "siblings": [ + "1589536358002376056411503361003254410290052284542099870835810171466349878603", + "14990749153165732385539429783441967578923641860222298344898148576639489863804", + "16378637127788741759121794513810490260086950198947199871507073933198864633894", + "7289281665665374186655236130989107785765734107958783764368735158961983710637", + "7494893404850284457199113975199803205368226008499111903804827754154651587168", + "4728583791185324830206399008411378917267667097910532497542313977183434258271", + "21510207904975983432309744616966658411875973211368192904041257798566731097688", + "18544880131379921977336715066282755360007376782643233952282242648182104325592", + "11350131885161054123891411740961859298129251128971075359384100957969251106985", + "5936572791062221247904373418651676105835664595359303610075244759616310715335", + "4078926070946410570056597962904265654995828449577504749322804457177063303011", + "4851451240429149317524019037763423810535033317759345355295897553106794721882" + ] + } + ], + [ + [ + 16201722238751874471, + 16810485124694736353, + 12029581033455218240, + 1363992890135371865, + 6580017811504648532, + 13331562348352764414, + 175391114290355871, + 4511939268193534363, + 7606255430335615911, + 1348570109543905448, + 15567020981576305120, + 11133909233779345176, + 17030646846725392159, + 10617777684476029108, + 8372862393639746904, + 3047325157961592620, + 13819128832200652604, + 4904768506233846983, + 7947662329797259482, + 1181024273700577696, + 4559182952058400460, + 9472870575145507821, + 13414808428735625583, + 14350774482347560453, + 10703263464886806168, + 10835681677139264345, + 1641102179166367563, + 1695785160455761320, + 14447968329122818921, + 1414964360005041113, + 9910927894724414826, + 5878210531969181506, + 17197830635709422378, + 12209859983224989410, + 2457576003098475583, + 14958026653977252297, + 15770177021332452755, + 612590575054519820, + 5358106577521611591, + 15644652778675976889, + 314044601527741507, + 16004895945996785324, + 13283335021960948027, + 13730224696212924746, + 8831487205338272997, + 10201887087675302463, + 7479245643816284952, + 1733016510202374617, + 13410453330221196774, + 9036756862244219474, + 13761296873863170252, + 15431987973648151708, + 1004526804150820143, + 14294850824899661806, + 8164498862425412860, + 17908068134016636426, + 7102809444598729193, + 5334325254985697482, + 4249335319625799264, + 18173883021591064534, + 12444788071930926269, + 475181629673159836, + 15103749780690849835, + 7526349945888764172, + 3686828191880750389, + 10516144921166731516, + 3451396183120633946, + 2361024864108012357, + 14674028997940997169, + 14416273309010098411, + 13848927033214714571, + 7406139112425413153, + 6082600951271773882, + 12784307074793484577, + 156733716632745234, + 17164276078817558014, + 14039764272166414854, + 6667447800927414606, + 5601526583311525119, + 1119885560055187112, + 9686757719420237405, + 3217054119369512985, + 11329478146435055507, + 10452098948376548752, + 1270008116363502807, + 16724535937953210103, + 6227752841861012422, + 679305551789562904, + 15353308108063606526, + 9390518247554202914, + 1874846039067959363, + 6128976267744985993, + 9824146819119416352, + 4644775409981682033, + 11101920649788161377, + 3342915808288625404, + 13444955492911798149, + 15015683529489990537, + 1515275900546828502, + 13308105981851066386, + 9525233977427798060, + 5484222372792705379, + 5459206304450265065, + 18435721897837783941, + 13434829935207992283, + 12228143945722505190, + 217978842531650275, + 15107769494466919251, + 16172247857224912194, + 8708102440752490185, + 4976498703180997356, + 4491749904240817354, + 17807411985139703027, + 17892428971250495794, + 2874227076011158118, + 6599556870172044127, + 12811525646111141944, + 14624081432736727004, + 11582619974876630192, + 3520320029949788615, + 14388729914674770698, + 15690901348662014144, + 2153222571402204837, + 12421216106379579953, + 1255540795942130679, + 6577856598320654025, + 6631340633430855513, + 18243120587854394418, + 11062009496568365826, + 8399220222050991232, + 324424421640439562, + 2217055300196340817, + 635978856931614402, + 16318539482699462766, + 2460940334315824712, + 8863145287808918994 + ], + { + "siblings": [ + "20045481860873745230766492353033512406103467232321487202721711083031630228386", + "4591065623801429784425848719079490757811385872302584979115555759650372191105", + "13476834043634083851456460499773093961922216440511072136643072890251759709149", + "17930614195884300747867246102393667015110952641814644866727315635613977475903", + "11061442020815595405206165126947379893319596015418203579522795086106359423597", + "3536143769225906982198218248481747577321049967987201436174396529482059156367", + "6182065849362253565170103655171850114435683085963818180684084413275029885335", + "10665697592985717838475230768269772602992161409532142644341469519103828021582", + "9891857481735571761297396601398485293082566260159973944004021094670821174", + "20663064471061475171895624567153629816488810621476725140626627725767494160848", + "7962328553757837920193024664671827465000296575537150928928229410163955423785", + "7606272583016731538439988566093235115677706480993970384070464174447254167501" + ] + } + ], + [ + [ + 4339854082062525541, + 11216978010090278610, + 8532177380328462995, + 16794544181671603560, + 11226534260942575750, + 16456763905313160400, + 3564592126140931125, + 6190811426216414853, + 6148021148459117698, + 11937813944437883432, + 8602973232367860497, + 7012011063799867498, + 11206941554263373171, + 6303083304777418239, + 15220017787016495681, + 736565718845283922, + 12153566176180464605, + 11279168068320235850, + 3937091339078098813, + 11398002117919859233 + ], + { + "siblings": [ + "6247927176675926400656363394105390470263252787290327287279075399559897672993", + "2035097974340876349794967991356829475018455958064516603766622785851536154724", + "7440620857598126503933377273870901893828604747316786932204480066895110255486", + "10132930062356775108446749988710677253826380725892949355983806890976729241628", + "5114622040813687890037184854932312184652719448027043993735474105274301888829", + "7460380825511670265183649200505858943101743461465615234545412268562028985477", + "8454588591778907447054548187053275061412475779561321111407413440613996823609", + "15711953481185758712447779666044225689631293507192263629186179195403646402589", + "21310978169095404955011776487454829092527247159372880040853962478065196418777", + "16514467428171332686647641106469620672835235223586887100984587693198767525877", + "6171089009229919588025699187318271553886071290242857010121039197275399388912", + "3695834156907596910657200631398678907951869053223671685327793445351339605618" + ] + } + ], + [ + [ + 12439316665958083645, + 15766047331367195191, + 16207259086595656798, + 4772109480479043701, + 18199222867886152115, + 2248471211537490422, + 5293088971931580137, + 8212658744866520672, + 16437152134781175485, + 9750985415030179156, + 12547450991084907414, + 1807936289844301106, + 7451723005147443304, + 5453340252032718281, + 12963337130161603234, + 17453243527252645848 + ], + { + "siblings": [ + "5668580613191391089757106267838840848973656994265750563683390709522959977291", + "8435341517561890430860341698438158551895492218953142073654286993947996064052", + "17506825273129689484997294042698598577491119134753366671247636147578670045094", + "632203346855496511360162037740267687800955461004963331143796873539559110113", + "11441990739937813144968809585586072507979617729888316532660403405546078985837", + "18711168241819516385927665537088894226899582967841765242147377140285519932279", + "18543887996605703530243824826164452666576159557605842248553529262180554257762", + "11301375503194540188965659457965508388098280531753264007164520524861402059977", + "17430134368608277296255355908102679489437034721136857536341245759339590824170", + "17433357183204279404252423000116357966713479264283355332543765185725050817695", + "9281253212237465152653768456918654183413487012627080861730514136150709842470", + "17139669106667366494501405449754846786315900841213795917513250017998618893327" + ] + } + ] + ] + }, + "steps": [ + { + "evals": [ + [ + 9311165090035139628, + 7911864486874227849 + ], + [ + 15712283769181087554, + 6779062863550153237 + ], + [ + 6202603420044067853, + 11782852671211918699 + ], + [ + 3375338667749451663, + 5009131409881582058 + ], + [ + 14437505188593176656, + 14634204020628882199 + ], + [ + 16390740030628268716, + 8984938854701989110 + ], + [ + 12076598592494051909, + 14382712228979650463 + ], + [ + 7828103266183645267, + 17883061538671625406 + ], + [ + 1658308824525283119, + 10406684945194538661 + ], + [ + 11209014943353841643, + 6306959654169136659 + ], + [ + 15005889288372536879, + 700025881647810174 + ], + [ + 16027810004902685354, + 8263581506360200775 + ], + [ + 9189252862142553067, + 4672355421467999640 + ], + [ + 14559671126932586649, + 13906480157601099011 + ], + [ + 13710786465508512784, + 17572843445589487625 + ], + [ + 4306570057059167142, + 9226574227235331368 + ] + ], + "merkle_proof": { + "siblings": [ + "16727650977002144981116555316281510316061662958000454696737840961318958147219", + "4901005990200690414200546504860481419599745480591071016633560656321193838755", + "12718262500576378128890921978673621148783581087903641770745664532447610589917", + "6388231879378085236476240978750404432997156864978823348826798545650197428932", + "19845454064670136941431487548963133440584297119226959943816794807022235978735", + "8025739077376898735442089866428777217118003123083505198887904362734030234479", + "16133163436074542098972792109792321942779475902302530076261787592418454329894", + "13531013533852933369842284620016165270465629708252041850544651139218758149920" + ] + } + }, + { + "evals": [ + [ + 12025501141917208566, + 1374559668988260502 + ], + [ + 12102335869866552625, + 7690765878633405656 + ], + [ + 5463703650188182996, + 2347108280190996055 + ], + [ + 14623761228396856625, + 13147727982440611101 + ], + [ + 9608966910259737534, + 17891235713862857352 + ], + [ + 11245190568058227683, + 3483708825480585732 + ], + [ + 14451584834098177310, + 8212224765901206564 + ], + [ + 6720764839458981451, + 4675522175448909408 + ], + [ + 15936606192891071928, + 12039820080919944052 + ], + [ + 12385808563868047234, + 98082163387308407 + ], + [ + 3313477810600271849, + 1546899430209999292 + ], + [ + 8968706874122666467, + 4331151130530705236 + ], + [ + 1243946639901221216, + 15422337037508414811 + ], + [ + 3965424218671620041, + 1199566879078022632 + ], + [ + 6240326974617561927, + 4584076112968802018 + ], + [ + 8544809121131699231, + 4860739972340684908 + ] + ], + "merkle_proof": { + "siblings": [ + "4224509639600583915800391265725041228640094090086372610113638600056702763262", + "2825247529651049722884191489504806276432529590765727210928184945381974473899", + "5450836196069305050180894258863892276466938764749838579989384169978599022726", + "17345893519685647809522263582670930064868353535147447430168470803817175320757" + ] + } + } + ] + }, + { + "initial_trees_proof": { + "evals_proofs": [ + [ + [ + 10170583876786309839, + 11770078759607580018, + 13945963428295615529, + 5034937171995154339, + 7716611614497392878, + 15232741979620568446, + 738004702201683432, + 17470436055437949884, + 9952455386307833043, + 1667927071168520316, + 3860656742866658796, + 1442854493684724951, + 12126081644111303684, + 8084958613392142411, + 13873834719127854002, + 11491422766844067999, + 5443476142809586525, + 3332628962629449218, + 10877939758144297634, + 10585130828619605403, + 4139491282512150939, + 2262112339263673757, + 6457872232523445890, + 6937590419441189367, + 13511937100309628350, + 7143670958764488279, + 2240075489808777362, + 11589006680907668592, + 14634873294732147180, + 14851371091772086952, + 12343954078339506504, + 3430916684649103580, + 8044688432446508289, + 14270944251891408473, + 10129420338761043830, + 10364976775744348019, + 16385692459864394736, + 10595058467921735768, + 5968115666152483780, + 4077475311063327021, + 15263488429837101519, + 6786593175835597715, + 11178333950116838531, + 4365337422258827143, + 12298524138804052534, + 5376491245137343542, + 14625502205063007181, + 6081483299316479100, + 8988016000532478590, + 8242714253111631261, + 15607221564042782955, + 13554318887284704504, + 16967174371064051462, + 17278344631596891819, + 8828736102298041974, + 13294371711285651080, + 8667325251084358300, + 12697489007207129870, + 13663389028761878252, + 15430545595198138594, + 598668660864568733, + 9626587844925945512, + 14902071257158171009, + 17569750233665245142, + 6141609835245235067, + 7366622191226741168, + 17763896597387289561, + 18340517137096313686, + 8841887342574883184, + 3568008577311889661, + 6208126303422327664, + 7036860875515806046, + 917002166720281883, + 12640649368786965675, + 16840296567337322063, + 9236213512557165000, + 16416376321227722257, + 2975815128683034931, + 16111028390225229218, + 3957448654672242572, + 16692132656642176091, + 1243751875193998423, + 17678396219610701751, + 5843160777449350661, + 1003418488509632018, + 16224800717419187334 + ], + { + "siblings": [ + "16163264385154023068715570102495552100313824527278964642699218180396959004929", + "4136096547844747668540063781950643974533300749189541916628184260576245996105", + "3370537060789150279276310898639301663956900234697909628475652590534315821922", + "10612382944659310091259978566324851734842528969309154028501148644053897045169", + "12560741689755661068788568036433854043729295746868365099629107420776180442408", + "2894821194639428029671138100403354240904009631966244138764111374528766244555", + "14333448891799729988769738794598762088448130347234210364670359796198947576199", + "15525760563933684700921114376158243313523667781791131534913375572407836775341", + "13216679426507849195758065838294957978902195814544669765133337445322180604200", + "20810789034158616121139762474488878926584975656509156722389294910361457320859", + "18725676953467858354143228181499990114599780342070276361469521285082260265613", + "4549838720286238978796090393936939924360424094271463676943313911074790429198" + ] + } + ], + [ + [ + 15085245511236255710, + 14105365480056215721, + 14601722618104759248, + 4470650368654643044, + 12150476587929342706, + 5349447319634068948, + 11099429967395711260, + 8243374810848096268, + 473346908793700569, + 4691905496058592738, + 11907933792350527243, + 6193200913434701622, + 11343425953208618384, + 5774996566629526745, + 4166614899676134737, + 16104034556988406921, + 6286533291232926325, + 3806717148698931205, + 6251633119387924123, + 7575754448459075076, + 14113388927065495714, + 3637938605013046257, + 1639040219683789531, + 296919240939451484, + 17910132924277443122, + 9798225816627613661, + 307468779903987929, + 7039441501523858034, + 8275131164052509384, + 17172803652925040615, + 11851303730212350074, + 14772858855690107380, + 12925638676242438237, + 10373256284207766859, + 13123570678068913848, + 14514008244985030073, + 13247020360545304993, + 7894688727571794442, + 12349403763114374260, + 481204777918028452, + 15452318349006418191, + 2334619619993307320, + 5076811437154903999, + 9355194224482399521, + 2286947688197386753, + 5209496666684725447, + 2928851062519477740, + 3418790235454465917, + 13367884653941825867, + 14934337199132924862, + 5341801955247466163, + 5809511832905772742, + 4823914705021283140, + 164394795936873887, + 7682641180313858615, + 11613658265890440988, + 18148839519329297382, + 17204040708417199677, + 12201878235977592563, + 10700266667317633372, + 11322980307031248519, + 17521460708451347703, + 17036156319136004348, + 1191156739635398025, + 7432877846692152458, + 1165416096229480061, + 1370361094962394232, + 11669773218264959575, + 9889906619967961989, + 6599589611719408494, + 1455976909214313559, + 14107295502926563491, + 7774864355128423207, + 8010190530977263815, + 4377240012292372055, + 4108827968831618897, + 15550109586959644355, + 3850291195651917962, + 7209327975176387754, + 10914087572360487312, + 18018092388269321821, + 11519960315878661409, + 16407079001608045563, + 7720134913129139174, + 17899328732821844159, + 9707766335079127956, + 6282347518921094830, + 14462846058248913983, + 4794592210805029666, + 17819144883466949858, + 15682463549361901268, + 6510032705403225538, + 585848250806609785, + 16194216733565946604, + 9168738353078119060, + 16822011586528455927, + 14713737274396937237, + 5745306159574699856, + 10450599663736304163, + 8025523842379530533, + 10475456836388562977, + 6037747228409067992, + 3041527416370950534, + 4937414182478620017, + 17850824480978386310, + 14620550814682619833, + 10335360533953941104, + 1299111279474102308, + 6675124903373020252, + 12725608571495228024, + 6344463014577408071, + 1258492690436045721, + 7327414090347367357, + 14865891855923381046, + 4789565698200285508, + 9202418306519922152, + 17282731969022454051, + 5832248640849522072, + 10107568245185671690, + 13822374347432127942, + 1177407083833344016, + 15921736578328451381, + 2407960617622694043, + 5268922010912595554, + 8782358750184423438, + 3908971193524003962, + 8189037376129846240, + 17134313518584420050, + 11574513940294915816, + 16290659402045404482, + 10619635426568595687, + 10182869896985759775, + 13206845763177783309, + 16728050896322634667, + 691048831000659501, + 8877791213796932884 + ], + { + "siblings": [ + "19580663729719084938745593970961662224862706038683968333127873642688023048367", + "15376388879692850868543135334276376682081469310433038962958943684290618735732", + "16018720384758368551256522032791701447245434051403920013786425847524162789976", + "17274940215768653682516260913605027589289131411109682616951427776753337708950", + "15110575450324740833658901919948000003412683753460585788849005366625725067569", + "1768455375255462064571549754470195967806406989675725999462887326837417438586", + "7840646694666627134816568694670558009336107326402900890372543140469657738371", + "20966996424241882562559921308021274274180783414347438480041868614649501169020", + "4028320631211222384141937473472112899484370773574475253166206569438255306313", + "3655996254125217972361261364818742372735509958214016154170760774552617971097", + "5980910974354154554130888133966171333002403821012200393927968310935282417373", + "5166281556435649325859688518200405850901777858662391616701238128625912212201" + ] + } + ], + [ + [ + 7801439444155153911, + 1485678449430273860, + 17371223254359160774, + 2008599237527459436, + 3818416199357842167, + 14952964357083096314, + 17738657789403162963, + 15760162083324269156, + 4556051519025608824, + 7168562036150733668, + 17518839259260856538, + 15194293949920275631, + 5899529461665940629, + 3387399011245856427, + 7693733266228695932, + 5335767647472544508, + 14484052533160627396, + 3881321992266398638, + 7134692189937597523, + 2883133082259510205 + ], + { + "siblings": [ + "17861744117236769389301173781676953005892272066509517282816970170435961296765", + "1692028049940831648488070300027873819799216209418390099408357174221272781122", + "18803012561871439883623094190258660305175828735003929931489169994633947448458", + "10144678701695610853702951443703272366441281755274185612544331006151398722856", + "192837078761396135290440054300203502203743703853667047053605546270244827993", + "15597082650265707660363515154006954897720328179809733659034730326248470764587", + "21480552315675949335869866760726205079780729187613145075680291688116283631122", + "18841766928108178668852407938804151735401849416784564914849507755260664276689", + "21441465356270438767467334185232221622260896889834729491190244557387045719849", + "6161982309036342524340137285222628251128678721687486276671666920528208950319", + "11083800187816206703932620050528684196068996248127236132989160764223808697714", + "12870315391573008137835096711970165669406092797325730458943504336872313806791" + ] + } + ], + [ + [ + 4760681013995708388, + 7503059234136600350, + 23366212727834327, + 7639031388496163536, + 16973531891744825076, + 9828971283451251194, + 5609536991235798811, + 4087312182240363182, + 4286298891205205848, + 17231778050388482501, + 12845950004694395575, + 10617091039063011157, + 9181919126467785546, + 17227500211204388550, + 4944977615017256745, + 3934875479671232852 + ], + { + "siblings": [ + "9682994137277795398286535071147392441467555301146238552679997859294730129222", + "14174616198783739767871629611175891010089701675881840720624757722491213995700", + "20497016690720435207716200997784126091127320485821591504418807914646377067928", + "12580527784728528834462700989124679847114657029022322823876698234327241844737", + "5130241197184820183053490303732133057990877314279615828545175976059379079960", + "5551067596236709883254671721939507959194281610968079961990543474213541480306", + "17704771008961217577776375239936621576665643267058311745523416200197473250151", + "2814281544778022690432314326543079517937916595347766915418547330416495363620", + "4706535671807329635984297572300299015586075629038633162835389805467970634956", + "13656446252233288083725618640033889445895316189342416494409815481739749863295", + "10376864723756128401324359071962899184775105551273518606363947585164556673152", + "8224765233836435539106779869098339195755938047123729052305837660466525028943" + ] + } + ] + ] + }, + "steps": [ + { + "evals": [ + [ + 15797691425542114410, + 17971732671147968456 + ], + [ + 1956730906361583817, + 8165625954627121030 + ], + [ + 2742689469794388917, + 3428464775547146898 + ], + [ + 5988741048113872316, + 1594464647248937399 + ], + [ + 2956821863746262185, + 6837121946175963801 + ], + [ + 17962061567118338447, + 7340007088245653739 + ], + [ + 6594267316030712146, + 12295135200477594135 + ], + [ + 8595973811636875346, + 6093894262979645762 + ], + [ + 5733119348868474844, + 9768030901315220599 + ], + [ + 14315284279420163454, + 7664880028755037501 + ], + [ + 391303449056878903, + 2579560302151260044 + ], + [ + 16827956407774995752, + 12796663394835091387 + ], + [ + 6327066790248886327, + 7554678709783045618 + ], + [ + 9479041818292876060, + 13026065782637052418 + ], + [ + 9097701579061923879, + 8892458489398019887 + ], + [ + 7081591369528511013, + 10081976687845700504 + ] + ], + "merkle_proof": { + "siblings": [ + "5811513471820455281508109242962628263859140358485213391336487951242876743652", + "18639378177912502988822835694780085640936440762571107119160498074170911625016", + "14040002202284233641188174957514501147558415623105731199410605752866725244301", + "20271216523418510146396114513447641524562284854798674042566393033720859803313", + "4690126141698250797223203705847104330042924335933423490536832238508327179590", + "14412285594984639554610061907660900400273508644628417070644421426614086041749", + "19961173612890285613810604612984146655745490474370298134485398024231546081706", + "4194004142688854141351114924801745135754383086139842232476121346077374880606" + ] + } + }, + { + "evals": [ + [ + 18242332448054373221, + 14237656752747797286 + ], + [ + 2822178310087896932, + 5089808140896268829 + ], + [ + 4418346230911111633, + 14205964210982072014 + ], + [ + 13141156326450266778, + 6959249025860401940 + ], + [ + 6541827416772565969, + 15874959410311368101 + ], + [ + 17378979001348341107, + 14181730312674481444 + ], + [ + 15330661703516413502, + 13658072217693945935 + ], + [ + 9979337245287297122, + 6753525842990674885 + ], + [ + 9233073886400293485, + 17447415654460122837 + ], + [ + 1310269388098804604, + 7552008189047168872 + ], + [ + 10706734317439815935, + 13332473260026812185 + ], + [ + 4149006015537759562, + 12103725220874881313 + ], + [ + 4428580476142658426, + 4715401434659341461 + ], + [ + 14044872752244253661, + 9947045224365429382 + ], + [ + 4517180244245430153, + 628962678633543676 + ], + [ + 9251859687135174783, + 8419327310945356405 + ] + ], + "merkle_proof": { + "siblings": [ + "5508939169340099809332686093386558719170069806031347706270297393325991746502", + "3946867440079609187717278859228820578719186780028390230557693557264515862157", + "9112969451155905655846651890494227500871027185457938924637482315077706239286", + "7466729881538616759049595582597912533058660743729066369590498490301628268079" + ] + } + } + ] + }, + { + "initial_trees_proof": { + "evals_proofs": [ + [ + [ + 13302645558419094747, + 16968278484183287786, + 9784850107063267464, + 15474546961204983830, + 10248826852570515536, + 8122760677460065403, + 2394573941152709420, + 16394082650902888532, + 14279596383056534666, + 7915116954248081356, + 11597222671304205682, + 15207393593757882418, + 7297628661710360768, + 13680869685153571408, + 11581599103041690013, + 15872740476193077854, + 1874638175734231789, + 18292116394159739884, + 2497340318965073470, + 6159936176736596034, + 537364591088643070, + 15131327861109486442, + 11227290103112475247, + 3568510922855902046, + 12910381289282705502, + 513558097201049483, + 827058045431685076, + 11677647978076304946, + 6483148455165940528, + 9646983589284031519, + 14395671491074777263, + 17483344341542140290, + 14887671112411539211, + 941852000138476705, + 5149213668378106902, + 207867497324723612, + 12264893459570295522, + 16877419596281815260, + 17288476900951654355, + 15473582505742595159, + 116101909007025928, + 3516135329678195529, + 16546759164289489596, + 9594800243433536030, + 15681451495873580132, + 7446130804393381415, + 5337231547944588775, + 17377603766411816465, + 4316614674026637126, + 7963440554009752443, + 12283761462267547829, + 16651674566140417813, + 9183564850608088046, + 9243877103327562759, + 9239214625967074485, + 6984441821625633679, + 11452771761005468508, + 8737028828014935182, + 5194123440853783609, + 2245110182202050742, + 10388337611381211766, + 4033173519051391395, + 10933134825418974204, + 16484749648637402677, + 5394147046227813771, + 10526252466565554226, + 1231743968582689319, + 13680075990879820860, + 163821420183325140, + 16806579152056411049, + 8714291519075608940, + 2166060215583928372, + 5867936660445405636, + 10000904967369748944, + 18163136970368095868, + 54957088430549490, + 16975004961373007195, + 2235770986214720719, + 6019922014474756022, + 1196172886619738014, + 6535217887815190794, + 3274004362829729876, + 9506048960735132984, + 1672907016084326752, + 9897379098914043762, + 1261443241031498201 + ], + { + "siblings": [ + "2725499247026329598016941509154434126591035198930985386724285257449543857936", + "19252901212800844040022234306408112080352250649649304972652779009530030969623", + "2659827589643848820605013480777471908007753892818725595397008567773321172030", + "4089650302333995150813946225407176659620124117871627835193300455248522543138", + "20166333462542927747023870984352309646360571001204689597771787939346512327116", + "8445491954231719241497923615811457600314781427938055990652034566843731638096", + "4336835774134748796560950294446508839774871518084426486341095921119480417254", + "21794439726773530931128005985751568146870236384856280682443201700075872572737", + "17157620011652329527719923994563197863376183445229189474791057942863050337385", + "6234171689816167762644001567559454206290105149644974101892010285050049288451", + "11962653073928804034288156006318453020283356565438547908128389439147802432972", + "20531359950793996073502242051998064322835724127990541525578136833693167734923" + ] + } + ], + [ + [ + 2467433412344499279, + 11266976777227087239, + 14849079288364932920, + 12471175335519960127, + 1052557560024266154, + 3012124075369002697, + 235397509069791984, + 13854189931052147618, + 7206460665114765573, + 4751251459065913695, + 11324678812107907772, + 258640154216954452, + 15318542705428913429, + 13838091500868172795, + 7962062126244497737, + 16035390055281046525, + 11386571279315572474, + 9358546457960895804, + 16197776346039234110, + 17053136203013979678, + 2804317955369943170, + 9025886431553740549, + 10202170667569926730, + 7986000238324142549, + 17328231636217097593, + 4412031343810837686, + 13379253956263962635, + 18063758943429992701, + 11245497200907118473, + 14908451166087391615, + 13785980106698941959, + 17756996223780877111, + 13918773891534190377, + 9006908685708504304, + 8278879238093800965, + 2017457094997739312, + 17444413050178502791, + 14363985058650880049, + 8191855246333196372, + 13735705980179767790, + 2398833671808950527, + 17587284672477888264, + 8274270521744168764, + 5731523952940064622, + 16568849290476684801, + 1454149021812830554, + 17450271646230073081, + 16449328328393839764, + 13118608351200601852, + 16436940773041953426, + 3758555228296254325, + 2556391727922586491, + 2593016762959019691, + 2916858915218721878, + 13293486833698388974, + 10740833862038161194, + 2112957902092677105, + 7821494702306385414, + 12152054146251806251, + 5140023469101078659, + 12635550398025993576, + 12769015001246867009, + 4539728351677002257, + 6046754161549359147, + 13816925610547512947, + 7068836248966186225, + 16738995702331295299, + 11555154470466352530, + 16933417716565285208, + 13529564519485184973, + 7538108352287364801, + 13238085845791243371, + 2250688446731581461, + 2107941986882106418, + 18166068049318919766, + 7327008533786589147, + 12996507162786371031, + 12676654072787020197, + 15611156570940985580, + 17722952663129849864, + 17699963590826942541, + 18046999390144526289, + 16551168589949339678, + 2737951381457117146, + 9871561605322426061, + 1712952029158494218, + 13804341105581865878, + 2515774586519545691, + 3055892671736160950, + 6710724628610805622, + 1412104293071317854, + 16497161007904304508, + 18357189440126213338, + 13603237157206851420, + 6273243960590211712, + 7944608681565512193, + 17876106042764502736, + 14798674142602476849, + 6953045780226967275, + 11587775192299104486, + 8475385210346705002, + 13371140973494856586, + 6794713226347140006, + 8193928063387091428, + 17367102755385777801, + 3555824590449181010, + 61277058838705259, + 8870120740632589070, + 8569261657911583401, + 11270438868333482143, + 4425327807117422123, + 1334182553156125781, + 1179127194588679902, + 17425871951496541252, + 14640393689292596147, + 15575431367431941091, + 10050699331787877280, + 15865307243306507597, + 1857750171635292322, + 18130938770314679282, + 7531133664044238608, + 12311758791340864819, + 8789821416232282321, + 1336876332854812867, + 5342090613788770253, + 8718998700193672340, + 16191452274236255652, + 4998135261355692699, + 13740174594907734282, + 14072068633008609860, + 16827929680059772342, + 13076448752571439675, + 1851555901541092750, + 6792956371094981827, + 14621930724363847451, + 5381649885728072012 + ], + { + "siblings": [ + "3697368111336814852788390728288168651761843580686919904705753453701564828555", + "8157863183369354001941938069666887778758163293015882555227352389208965697111", + "1839590469573502320128302052842569992161612731512161799915968707286194703851", + "15047361250661113398165673216467740394985222842468628270022890891741699067659", + "21174222224001178388501637557557075080272806220542533088437328642957710517011", + "13432454802250197378229694329139358748625217453066438865814518810679620628410", + "17308243007607931392560875761257971165048022119941135309877616223503237510425", + "16132417511118675772563615171705548345419868528894219693586552628653715793807", + "1386086069140630774358596478116050527874745004095021749322936924108264414206", + "1887113020360105652662812427880509995597812140399207135792857998036172353772", + "3286885105992486015096575778995364139525969434353456377206180492469920581835", + "4431994467078885193534287713040019539623543927214747668467426506317824549569" + ] + } + ], + [ + [ + 3683188128712646696, + 12467685144645901173, + 3829247226739253309, + 11589596607452418968, + 12105001842505782682, + 9731988610523704105, + 5527684778445703634, + 18161861000759996444, + 3556301222686362873, + 14701887422977382633, + 7877082953418399853, + 8304704073725917169, + 9236320453600710822, + 15168437757002237253, + 5248140237912148892, + 17167660376072466439, + 9875997975569301478, + 1999852464111255151, + 15868400892755244257, + 1440201915165974408 + ], + { + "siblings": [ + "6006792668377631579079480884740813784551388018205455833443115470906591536259", + "21056537149526526853087959820673223945389851826564881863246899994023312212220", + "15589564816634872854639756442693541136733153867564201707661369253110481577131", + "19105668431886128482629007158206621112422205061909915258665916535314190796080", + "8443215089728716708871084254062468674644827526379143323754998070607134753149", + "1516180912539113420217317531029129393047750480345640338926174643173857446872", + "15394358855171916606818974612831102038420851935760713629460276327597084752187", + "17739394223634583180839353078337463981343720689948270103099898079500917532350", + "14401428311962827617122497726728990686497385601203540994310204184722476410946", + "16319416607368778824146076811428585486999464678118616846097702868580577765723", + "6417694127983343415708748850913706642961493910752999424644393788499915769981", + "13377651578165513377462559574843959840121154298888589073842056219127158702907" + ] + } + ], + [ + [ + 13266758843258597621, + 11524647466422745539, + 6881340121169116593, + 8361097529067124805, + 17479554477924179340, + 11070327993863328904, + 9085848150639917536, + 921587189891868145, + 5400594063063277408, + 475583497948677235, + 16008705305925417402, + 9883449643817523252, + 2732154728014245124, + 10430686024590219255, + 10945407543702064531, + 3239449221117925091 + ], + { + "siblings": [ + "10508877493953398501486261658717128535317979548464755021716086407735252366883", + "14628749786603096424085889464486827231421399453569449407870586792199040142611", + "11207154699944222060193713560946496074773430700259799973107333036735353714717", + "11634803605374805690460571165452974362094861316564485413160465776930463497382", + "11290373769816903797364896564815190288511924406171093486486540882482124910003", + "5092803856474319924088713966269373583178616244888741249805013702201418534769", + "15057620251103845515503055690385226849177583130461484946078690627836345782579", + "11004420214184090588935333835186990187665516193765086184121312359133702454815", + "20305214852888792349816420605314919197087114385857086863150101788064056996267", + "9120420177945562262809230157305952963714133849611147655590585851660810636683", + "2044839066128482766125182295461919563725900701414871958767730750516362397451", + "19478007696468472378947095585832669160587463101328563412919982979727141863767" + ] + } + ] + ] + }, + "steps": [ + { + "evals": [ + [ + 14215483258861457442, + 5358912655976086322 + ], + [ + 3837215943743474350, + 5032579098721904478 + ], + [ + 12061625551178813635, + 12637524556866737255 + ], + [ + 16348790181836052495, + 11098927449634498205 + ], + [ + 9093367652456602441, + 809844341636108722 + ], + [ + 1053309584707248559, + 5662365189213118823 + ], + [ + 16647350156062223806, + 6936100629840990525 + ], + [ + 15478410207280199802, + 7564245659159206614 + ], + [ + 4118327871118298820, + 10999108633881635179 + ], + [ + 4197760280264106354, + 2632556760845131863 + ], + [ + 8545605110922954107, + 7651959429814110647 + ], + [ + 18391656052001680148, + 15825726311216338585 + ], + [ + 8370632460675782059, + 6316475397634499756 + ], + [ + 7540086414202595476, + 3953432518698668496 + ], + [ + 5419921352090263484, + 9416038568362569180 + ], + [ + 6653094586225653952, + 5982228434403769413 + ] + ], + "merkle_proof": { + "siblings": [ + "18443438744134526597529804478579138694838270940402593266579320488085829074592", + "11914111249423060069391263747022207701854899243759262535925522908563821071004", + "5724794398949496866109446239618311587622344428279223745579943183160811213354", + "10866805764302750656284383293974010863753862953000623619715940295202838851645", + "19752785240924197641511030337158966849880061370261642981349645477205969067490", + "19017160272964244606571256421197399569122029065061779313078625445868508660836", + "15367795410620928620656064141176785056908859475931333971843347997353820934007", + "7321070812872538139583286468340546406302931780446571823855108346772507123318" + ] + } + }, + { + "evals": [ + [ + 10527386003116779936, + 12717581320824128559 + ], + [ + 15265325084834169045, + 4953987769933598223 + ], + [ + 3658434804870366650, + 17103819900358128221 + ], + [ + 14569392492214655110, + 10561209245844374528 + ], + [ + 3288625335150295057, + 12693107428571225939 + ], + [ + 3543029827315268915, + 8352551800803475387 + ], + [ + 17797743807185141632, + 10208900942252309779 + ], + [ + 3462737020138368028, + 17210343836005822201 + ], + [ + 13371016901149546225, + 11182314746965963645 + ], + [ + 1222100973805861319, + 10211404401888183733 + ], + [ + 17660786208732000594, + 14623350766271575011 + ], + [ + 13028355032435200831, + 1037154490891665830 + ], + [ + 10854229741331275230, + 3514197728880625967 + ], + [ + 5947054438879512012, + 15356955295129210140 + ], + [ + 5077155324122659025, + 3066726772964842582 + ], + [ + 5144805648943486859, + 1872183940816355051 + ] + ], + "merkle_proof": { + "siblings": [ + "3172145761683187120348398457339206378840292277400553830431466063149428577731", + "9109703345088123836776487462146672880648486412140850410640369749113021733824", + "16839087879754769622404743522996461826534858399052598393758221189892642049336", + "3954838897038586814831478539703227450385433962414363736232707147744602217656" + ] + } + } + ] + }, + { + "initial_trees_proof": { + "evals_proofs": [ + [ + [ + 816966575502908625, + 13739137434682851092, + 3748260162165867176, + 3573452037414992372, + 9795808109947279476, + 13689451723701677465, + 17314151724430987730, + 9012473154108476279, + 6333230180869081318, + 17971105457324396150, + 7446304940268182403, + 16180858585051817731, + 1520799241454846826, + 18425742183617687501, + 5027617492403143518, + 7556522739920000779, + 8544413501234354790, + 10945227925447884825, + 5403860809316829836, + 8340568775636287648, + 3468695531789066414, + 11385399589668726975, + 10598257313517047623, + 14682814558415744024, + 1006781401459189843, + 17567172115887402812, + 17241867512931936699, + 10265964749169798818, + 14980333400582561653, + 6360374302246176655, + 16069099431706544778, + 17501784017785582646, + 11165319787843549292, + 2626593543712647842, + 1046248321135325288, + 14649040027220830259, + 15242912665747560199, + 14951166812624717390, + 13784844398884325130, + 6487732362912140571, + 18175922897349932692, + 366008292294003772, + 18430872639589658040, + 11816235310570557329, + 16102540357027138028, + 15516441849380410257, + 12077949524727284437, + 7182067711226108286, + 17418180637794852057, + 13546609299096646003, + 2139706623551184693, + 13147912099407339008, + 368169579770761821, + 4691978176686129864, + 5047752499929099758, + 17008600867568204774, + 17665863964334305820, + 5411143285526703232, + 4552606648434548532, + 2790456448416056883, + 10783236539348008510, + 6566154877523792415, + 9659656954391585663, + 268078762949462183, + 809911139215136132, + 9224907792186201833, + 14717580622482496473, + 2265791429323254521, + 15078934993859761272, + 8507060926563610130, + 3331384390127358604, + 311271869691520019, + 10280610691810964491, + 1563499577572744021, + 253880306352032795, + 8781551432009405684, + 5634194603834247035, + 614912347982771461, + 8102628679178347551, + 3870633393910337231, + 6416117409092160644, + 4070430618106310519, + 1570120673801494168, + 17247424106127691603, + 12760902656666189349, + 862858815052081301 + ], + { + "siblings": [ + "8038768350648278507510489963167572943349405595996110270549292641423918517072", + "17697447703999180443198777303811389249127313003377914011435427570630676229737", + "13094770977765618347828050512305671603774353091327524159213698151103356630426", + "18007898371246949690915084438164135281049638610995142104741364693344849884755", + "5534389004193646007025728254824218683543179695489623191405327247495744054930", + "20202719127821329512747780304114666718071843473851671984134832997168787390097", + "20762413880622961470864672857632952030303196093018742380164480874932229427046", + "19872858986027331347985931765060039222134784896324218122230031730271873724007", + "21222462953018837000944040835278460338495254586931463515565941693734359693852", + "16161734346886839066580759269569988426072800467547078654379842021330975028130", + "14790866537153301742104832383429216495644393732360404271733140093406907334770", + "17950634223319622329704731292629967195651718825833605390927722496175392367218" + ] + } + ], + [ + [ + 16698693854273509522, + 10076477062764003502, + 17372795036780126750, + 1086953963391970603, + 12060691964737803600, + 15096224618972512845, + 17644828759874173438, + 13651663710301680017, + 17177461238189384251, + 8022695171654562086, + 13048550118406815682, + 11978962366267161773, + 6072373055073779521, + 480539041242116849, + 6418511813337920067, + 1631795693424888253, + 9645266971435691322, + 6302108416633070732, + 13867212634489454095, + 519445567371721003, + 12761340873525850596, + 4242465700196005747, + 13962844016426364259, + 15515717685257142101, + 6310288882382646367, + 5331315070774697783, + 8380167720660971396, + 9370905868703416061, + 1086031868131688147, + 15891783555180570094, + 7249738367058843984, + 9311591847150019147, + 772381011917450993, + 8739658681004456866, + 18172592689036751947, + 1242358048671325140, + 5716277755122648287, + 2731873984003269694, + 10314886063555331023, + 3267487889958780030, + 14908983521068035281, + 5674625346081970733, + 7378417316865348043, + 14010160800297760588, + 5403323373651033939, + 2999362436385707281, + 8876869481905702376, + 5464732013677615732, + 9866475316183141129, + 16982553415304829192, + 7510585317382644717, + 6300146331677341690, + 4773871578359776247, + 4127030455769786398, + 14604348264105656060, + 900601899766004304, + 18341187149894215999, + 13363592353309824369, + 14550308451950467019, + 15940367878533794204, + 3317000653923792377, + 12153550960599582677, + 15451064313066921954, + 18302478994501433204, + 13503436300936655082, + 9638616620162567477, + 16537217656696435275, + 13769794177942657205, + 1444792209665774992, + 15624549932143185026, + 11091313384814095750, + 890883892436750946, + 13278341570921601012, + 3792210366940416817, + 4764304747316203020, + 16261367856148474304, + 15107665595326096967, + 3544446739111424327, + 6460098674839471654, + 1769588218330433411, + 8141657173376424663, + 2985847720100753607, + 8076127471467592248, + 13391702090330963260, + 4541547963569333426, + 3752882409835602189, + 11623173903108902950, + 10131216223527575155, + 235343826316296478, + 11962874415156712977, + 14102968161243857261, + 3884430610016458442, + 9583628599003235416, + 14020445713111945850, + 5446069400759269789, + 1886310166784470989, + 13889283374263870879, + 14047731160807169014, + 603790461100215638, + 9369406014593167741, + 11243705264489208655, + 11639448046568895546, + 18119115497912328355, + 9275432280653259977, + 15552607616915832050, + 14623838028671059534, + 9712245580847921207, + 6804649288888948657, + 799019181869549839, + 3272290811289444477, + 8890169359285896107, + 14099528374689781087, + 2961158610865772209, + 4470184064082947464, + 10528820845446677822, + 1584504470025421367, + 2200111171272118535, + 17550399259178810120, + 29629426897689527, + 11454603159682982795, + 11388872578124720371, + 13176145238800185132, + 14455475914960604532, + 14423892606232588970, + 4417823540874278651, + 16298450974535041965, + 13547404883901632479, + 941994824290392081, + 13440734859798070248, + 14777740904735321864, + 2784944725237200139, + 11009019378518264979, + 6533834755130885861, + 10886479079433680996, + 6456855647631332466, + 443804028526465210 + ], + { + "siblings": [ + "12118613567991902658917166916038754787072601441339271493227759082458810999586", + "9879485143381785365197784946888246884025330708767048880980257115008958187574", + "11233561999647536974673518422447654352015673971367641285813834661139513282219", + "17804786973377373936555778826726348642932608090605842950553072800944409519472", + "17643637648119810665988558755256484476991183702949982629527933185647596166227", + "6291200532899956964626663564845351217028538584550372932882607031151266598175", + "19957590123095811777061049119752859740164973115540742164659106299698010303585", + "871317569414706876778729673729979179702229468056488962356839710946062344150", + "9077583765453675916908904392191652329463037786998559425752309014999790393633", + "18653685608910287092963777951482802187328071899271638347191895051342227833931", + "11129864197318451568779033932899456075749727848542960271538955390154766635147", + "3636581569219531739912161427607159246780863289792252879860210922037232236105" + ] + } + ], + [ + [ + 5502175222526387898, + 9331905584837686103, + 8499646017529160316, + 13616984649807804579, + 3697587451501151326, + 14906595063507714995, + 8641805759288448952, + 336975553303479122, + 11304546579383626729, + 5315735543686835748, + 7495938321949498401, + 3020782164272668961, + 12382370330960853350, + 15959026541867486046, + 2454797223635909606, + 1185470679147293230, + 11617652649143899595, + 18076477854341159950, + 1279129376087016363, + 8471220935281487471 + ], + { + "siblings": [ + "15101007715110811905507626739290616985152677981587400834271596659116019774650", + "14649336013878132088924093626941761446173736488005474834373647199674378538683", + "2959110175505492565593198201651943913551476715258162961626252463777503314136", + "10467597850175704845540660193503049324054865115152382614268985230356494181409", + "15280519176543216033012366942582284952939143006165969265104958988326440067047", + "1706158359483390419594777968044884902704360073508818839947129688845566857117", + "2645076654961288318733702669063583802602694552061823693215580879224244187514", + "3858503536364242452240809747408002765632878570752398552443592961693148311506", + "7302894102162114363858517757110006059929667854129212873481225029050177967088", + "443096705640459275797608996885456308888976611838295867571135358989148597146", + "15567669159759363608065750934779267437804507982522508629540007305620741726809", + "11727423774764093614628294043328647616845461390676350431594059447461758141477" + ] + } + ], + [ + [ + 2944896318701236769, + 3005059784588422829, + 14281663045842522741, + 681974749565245608, + 9159406685834911726, + 11625863375620420118, + 11385283449101687176, + 15943671826147556096, + 8465286333662570105, + 3845486327400705698, + 8254326874148203924, + 9131649431886694835, + 11558342902179890805, + 4531778029502598456, + 6004699682593829956, + 7565607605575342939 + ], + { + "siblings": [ + "6266339348905757841008898677734170285096437149766311539180211382776452335642", + "3983080687028152938696025454769598928447542949830613411213234191194119954898", + "7423187988817403876922982306906316567954222061131948844908865318590847336554", + "1598229318453610185899950074995969304955486804265713995410627114039338948014", + "8511041222295797352765917775872874471877219236549712274600775983034094863594", + "21179837475385335691998682135000810823283559071694318491989823723624792964250", + "17278757121134887726736406778543216956905293664219676605733202171252094079008", + "7758766096855414622181941073202045650782918116160128492180561072882612913445", + "13857458492096094520246505476106641207352647095350229673390970124203280743079", + "2935901580961883212036515384542853511266991277587537593361499967437037746406", + "6523303440334037387409038616165614737764697908953778855127045340261474146644", + "10594202422010032864593439952098298620708873344624604945378076356207537101989" + ] + } + ] + ] + }, + "steps": [ + { + "evals": [ + [ + 13829584444053578556, + 8224607172300838252 + ], + [ + 3521302951853942980, + 13113815127972928378 + ], + [ + 16280588722162421900, + 10772329849340847164 + ], + [ + 14359689256170193350, + 18193375376410603298 + ], + [ + 12844327192394170519, + 16891592083178243981 + ], + [ + 5973422044745993657, + 14746796827722238984 + ], + [ + 10970074178135088911, + 9095402323562299389 + ], + [ + 2677526076261686553, + 17370184797331710395 + ], + [ + 12839367519245526007, + 11181552175474338922 + ], + [ + 9889629847573689130, + 2348896997719068487 + ], + [ + 15910309680174567138, + 9544635065734993691 + ], + [ + 13423697222166905918, + 9155585129743248624 + ], + [ + 13839078469693450315, + 15870436532748124244 + ], + [ + 909593224630753301, + 3729857325373607815 + ], + [ + 4469319517888946570, + 5904471552712148270 + ], + [ + 8461485248729632416, + 5105349381241530834 + ] + ], + "merkle_proof": { + "siblings": [ + "20627370853258370528942388632627220406457549653654021584206853158652867182792", + "8581341253530021178004545548090150767890335083900079629342510673533964573461", + "19817292039837610690367580604989890212751388793379448324603799213750752927699", + "4124947629097176296005433434633980165120262559107105315722972078600714411522", + "14321865028566449935851734930372511042232334395057015359316565407784095861645", + "12150489643427538925422902511399244835899932075696559054943216218339240408488", + "13810803587131434463501260849998707224683751784444632564877911214290385778048", + "14349890324297666163526616088635582464619401599904225586860293609527870241067" + ] + } + }, + { + "evals": [ + [ + 12517080778242316078, + 13888790279779487088 + ], + [ + 13064688961979292930, + 16240035096113947216 + ], + [ + 3514266843353878828, + 11740729953706976482 + ], + [ + 1446025082905998661, + 10652787645278639259 + ], + [ + 139816771683627250, + 7124655672630544869 + ], + [ + 1368750152233665678, + 4363425218854938100 + ], + [ + 4078117116800983879, + 9245163786131604960 + ], + [ + 15471866022413127812, + 16086679832954518238 + ], + [ + 1194583552237028543, + 13293546885255652746 + ], + [ + 10864299636426316968, + 1019218027752127140 + ], + [ + 12524709285568094656, + 8830977233450726061 + ], + [ + 9686068459398577776, + 12608827376592136402 + ], + [ + 11710152598534123038, + 675795800169665108 + ], + [ + 15059447646372707481, + 4885816580410366335 + ], + [ + 5708736732083031508, + 2579580153481950183 + ], + [ + 11232540447681873479, + 10096382856754235120 + ] + ], + "merkle_proof": { + "siblings": [ + "9239179178773580459677112639613332269814367014316076685639684011008977739349", + "1996526827138212029268205235003105638739520759823740120306044422861748948644", + "7597018127751899865320412624422736732085806259456237163892267725665121830284", + "6994498322311443900363168998981388864440163005004019159867196268673969759353" + ] + } + } + ] + }, + { + "initial_trees_proof": { + "evals_proofs": [ + [ + [ + 2822330103222455380, + 13413848353869141418, + 6427999502107331951, + 10583508044840080723, + 3598154609397688402, + 3404716428094996177, + 17478116939752638270, + 12211759403564387753, + 3558967080946185933, + 9049851970123830362, + 7052353404345434468, + 7195390318390853487, + 152121291441467298, + 1784452854657041607, + 18135895795348556728, + 1883155269899557563, + 10834625064180872254, + 1564485506958353383, + 11326737321163445732, + 14854209336953832840, + 11829647619699008670, + 3234964099814406732, + 939370414484765185, + 16765574466393461255, + 2641458261742484859, + 4391208473658026599, + 10982111271425427078, + 2690522135302674440, + 15097739522356100551, + 5684030706293509174, + 12214958553003204781, + 16286766807882884872, + 5985915493195744851, + 4029640542946071316, + 5457158939949931531, + 14876732000133741511, + 2710915429168262781, + 11967847122642859752, + 12053211554554821477, + 1854299750916899180, + 14549652615890468762, + 10141189858239473730, + 6415119076622350505, + 14691636754206836048, + 16364551108838816702, + 2426978615138909594, + 13185848209774207503, + 3209060168917716067, + 18106584750790185772, + 3796521272694114438, + 8032264526415337037, + 7689960827455455892, + 4746839744806300264, + 13683148153682599144, + 5967424809482001020, + 13199533525760392303, + 4911752602429571604, + 12144584278719984339, + 6163283446988533343, + 1241793324629602078, + 13597731454295324120, + 10686087955898256733, + 2334382413026952032, + 2079000949090189197, + 15816068748212614390, + 9642895753578614666, + 6299025967175091461, + 15598558838546027650, + 3560828133349928923, + 5122428577742831189, + 5944937260276629937, + 950492558291136463, + 14186034464873840706, + 1368490889051280669, + 2256648568570262147, + 7718346111546660769, + 3014371004780561785, + 7906467974742437661, + 6291526913191730514, + 11888701006362834315, + 3346561226370639111, + 4974191225276714615, + 15619358182980993132, + 9002202308983657750, + 6820043150937309678, + 10795723218159327532 + ], + { + "siblings": [ + "11022594348443613794167338549745549992773517200881715561746540928544674603449", + "6329697931857990521590368206076663755106937778067863746781598643255950664553", + "11854570232603776769343592233480565008336847998722394626180184414680731086821", + "2148578389783666363780319957504433531083098478227167800232066521385656694885", + "16820035980226740115615664050846639025035976412141508866318886941449050942098", + "6598949417974612315767164530788115069222058402895645359120039328112710487566", + "5880052544773502833278013938537893706147575834290806220376762103177166065760", + "20668979027614388574236197270509093678205033549028930380911453699625977417016", + "11177509397249187423866243907927679301428325004525476105040747143512940841650", + "13464432272958455990801494546682032226813431386723499739665108259305692500104", + "13626182516546008545441266211677953143259759646987714184038037609612089613554", + "18336556461154158953330734156204028673801247292781606589601026775287021707273" + ] + } + ], + [ + [ + 8904683884191881932, + 937141731292987928, + 4887302035464954923, + 14351951515343605109, + 15993964841816573094, + 9102212781937391871, + 736511604272140089, + 12449262215875399630, + 18180161417585385687, + 8913140766247142323, + 2445313189663443887, + 796177280864413178, + 10504150685456983341, + 14214672405724348518, + 5209894540757641886, + 15192523140659374361, + 5221341635413212465, + 2570075641807005929, + 1851997663480859217, + 7651297396386524968, + 10112846698105610004, + 370540076032674778, + 16345015582274453944, + 16104491428094804457, + 13415539921454397087, + 1759498673100227682, + 1188673138079118317, + 11911932336381219232, + 5507289098056456309, + 14783338061107110991, + 9298858074782656378, + 12347038452355777738, + 5853822604203705112, + 3438816611634986722, + 9335625307900688519, + 664474707768529354, + 6557567595996719548, + 10399352927201169675, + 12586171585086673162, + 16279756021334431586, + 4032006162473830412, + 16120981678920079979, + 18324084377952983121, + 1057719504539809389, + 8384772366890920115, + 1568040999137077342, + 5748814574923874004, + 2410433475317566153, + 8001667218495644541, + 10574609383618967741, + 2240651566972385850, + 7148979907699337727, + 6565861958165820761, + 8137420072624012860, + 16134966133889470318, + 9906614267859333880, + 7209036713873110695, + 8810203929181520792, + 4036208577501653241, + 15714168281259998049, + 5459865353831644929, + 7224344531987084773, + 5846206053608607968, + 8539284616905849870, + 13845957802486371353, + 9651440986195753587, + 12398611673145972162, + 379163639257359494, + 5033351054153096048, + 1743943254879997519, + 11326300353958823685, + 11211663620316590001, + 10918973609590610203, + 7098554009942466701, + 6470970369795794941, + 14783079368703233120, + 14129640983803904281, + 13815768619163966002, + 3233249704898314298, + 1149414005783841136, + 1980655067740958903, + 12207182848378732829, + 2251517083070870118, + 13558224823479564403, + 12264328585947996109, + 1430735009090568596, + 1703264457396312893, + 4461817124253947113, + 18331692729081421525, + 4833049974303521916, + 8974059458192483581, + 5428006970907097975, + 1841065585123497262, + 11572748539871395923, + 666483471886288855, + 4182761431840726730, + 5180657736706313298, + 14369686350839792970, + 5877152742874480866, + 1429995481604378887, + 7789452781833082848, + 3833006445746821609, + 14554418807902457419, + 9447443502020557849, + 14789031759631408033, + 2392381852055191311, + 16879020753284226776, + 102598629951337083, + 11626283456648875089, + 1937797986042378017, + 12089310980595776598, + 16381085896305175572, + 1422513328480133715, + 809740522338474548, + 15848234914216000457, + 11914061312470087710, + 1819456491826936008, + 16363548938954722927, + 3487801062316674764, + 2695581105875638194, + 5241384748040992955, + 3206968745265379866, + 13953045831907449060, + 7112933124970409103, + 6158671885621906777, + 4436062711354898886, + 15183564204773861373, + 4523577783362465359, + 10689069130352899659, + 13287178834473489680, + 10646035193627318413, + 15751376732884943157, + 17570895642954201768, + 14280222274947786880, + 18315807611407777836, + 13520953461839659079 + ], + { + "siblings": [ + "15144621796573979329824384861819723231546097636879005909362064186937732081683", + "9946668984240041755316774038171494230023846283623591821508596723932467859891", + "15442785423400129258729972750911218575583999252075508411007812130636437091807", + "669172937962494333208796471759416826803361726007955334495343203172918704339", + "16911880631699393137002589218259702854838658113043065922796740523710583222278", + "5413508671892604543223448187613366575965486840162240166368963716423070135457", + "19241427957278554981038022880879113885610548387589047518149053208448257208642", + "18876618593031819048346458250500957022905289068562761173641846630219662147111", + "13360679128016524553765006585316081770155110015897555430873901548782766451108", + "21029328147840758006279956566383052454868899303432793788305099912922565952815", + "15838641627924899601809214711551815712459467495165214831705145438590137907324", + "8385127020566588343035272683843043969904346010819239743097190743264563524917" + ] + } + ], + [ + [ + 13539304489125796223, + 14791696652856186947, + 9415279856370406562, + 10474959699474938470, + 3165434293601983872, + 9817191753373754510, + 14698741503440969372, + 8697458470134417712, + 5954477004080320659, + 12898841320575572604, + 4807033278258654656, + 9527177892111596, + 8440883035505417028, + 12783753682033444737, + 14648327853844809632, + 2297228886290501832, + 35698699668093506, + 13061862432681918201, + 4026396885387600907, + 155683300182484418 + ], + { + "siblings": [ + "21589466943213278405202188967372184469264696712451675264074310413536941784300", + "11479994706763379949253554412109950411882680868522759049551310402229160605657", + "13336599447387555677719831754534397272651919245191084040458510041973096111595", + "5944477767759139383669608586810850796846666296072908492518168378557503557562", + "18958015994035756541223723091283957560620203896482177032245627340948110349444", + "15975816519389958799422692784413635268660174308150457526838003303027786241458", + "19063612686375971523693214360849634345122370200685212304278068585780429311411", + "3577818545397736460378974083598822397775554147752873003389354499797461340100", + "12461027781127339057458781731881366727607967042113329035991998134441687764030", + "11320474509569010967654753891558866771883156328266655257193389965468446197881", + "207053273334893087438744904862932316816810613535574463279061807390775550865", + "3798814720411754597177065328948895690125186800844657363837407494785883711259" + ] + } + ], + [ + [ + 472934323740048535, + 9914987904683166153, + 7335923101108032666, + 7754731261818812052, + 6056262255459657378, + 13632157342322621790, + 7012693242231257832, + 15351333974147701624, + 15513350975610302452, + 15393303751635418362, + 7409580146540244775, + 4905817963585412489, + 14859476596571445260, + 1440512629388671797, + 1977136507793261955, + 17268421643254618050 + ], + { + "siblings": [ + "12042834373950274575969921322599307218135359532847082028155299437363502887823", + "6341109674899783701166957272170512986988763022524003362945055998991344761350", + "16438474424442019914745955657864483241557413496464818333314780889670679005324", + "3952477100892611722386499305284459284471893140023055649956357098604313292026", + "17542986099331025229344946176370858023626678210623947328338183203953339044168", + "3647933391539371822154152590175926435485636350904043828210939203170395006368", + "958868467079808296416727455226213850112986173859373754978769872851690941609", + "16495931746017690186537467465300154713899832006365959847771099018677752030974", + "6917945539397871154914372785467066900863022558114203349513634042369490936546", + "20092638972099432990612247148709477135859354179197353904114017535653498979340", + "12418355499164068352223083900760317432399927256192105675447293382063085500715", + "19524790869652984562395980257533701695017908079884155559094358581488948384180" + ] + } + ] + ] + }, + "steps": [ + { + "evals": [ + [ + 12133709208548025872, + 6601017562127262148 + ], + [ + 2209936986796152885, + 11028702223676832799 + ], + [ + 1990838648583356170, + 3678377876140384541 + ], + [ + 4454115131772105312, + 13032281875348697662 + ], + [ + 8338611634888118203, + 8978939248160315530 + ], + [ + 11568307339659169572, + 8370779245566973393 + ], + [ + 7814151854712050258, + 6493977566769133302 + ], + [ + 6474404946852141350, + 2407656677688344744 + ], + [ + 3119725465144104278, + 3107461375659937340 + ], + [ + 14407872984283367051, + 2975767845588736845 + ], + [ + 580907717602102726, + 11798561124577381657 + ], + [ + 4553575504885109308, + 12265134738480174374 + ], + [ + 9850269089954553148, + 1952713700518956930 + ], + [ + 4531815362217582799, + 14829733579610072146 + ], + [ + 7967268085761108355, + 16669480598458240272 + ], + [ + 13946673892008974577, + 592351897333881970 + ] + ], + "merkle_proof": { + "siblings": [ + "10318665716670950777630002826133908194228540311790043815683117515613977740366", + "14584609383935336030356586449823167119520085374349617744797161647445248749877", + "8135108212901105851946514208220173735105438507177932337111205333550527558579", + "15772016295607828040575595177025854770245524916664300579726936185438772365152", + "9493869078229386906842866674587741026873843224822079050472220901758332661660", + "12243113411527617263025435191082079131893270372595729142232060956453479859249", + "4884632364912187727934868162802156489598860725009461635207313166716858977996", + "18475098617156176236145675448985833706987788030213443090611745375016487928547" + ] + } + }, + { + "evals": [ + [ + 16034888820823588367, + 4106062736587546107 + ], + [ + 3742712464324528609, + 4068648557968802275 + ], + [ + 16549920098037788781, + 8681288129041557591 + ], + [ + 17110589594259433206, + 18431937966206205815 + ], + [ + 10277946988465002688, + 2638869104911590885 + ], + [ + 13942574682589816788, + 15925509767592223092 + ], + [ + 7143700694812155745, + 7104429767553180914 + ], + [ + 5608073404120144789, + 811173091931933461 + ], + [ + 13502525015643834325, + 8097209461337728881 + ], + [ + 7278695757606952935, + 15197564953124797519 + ], + [ + 9503326752327934227, + 4353259597036744444 + ], + [ + 15131812678737547706, + 17299042969962653686 + ], + [ + 12114092790638506896, + 7888990636657815071 + ], + [ + 12728953468078258412, + 11876472226324363942 + ], + [ + 7542055036636571143, + 10115107116662005370 + ], + [ + 856405157397745231, + 11698267250034259426 + ] + ], + "merkle_proof": { + "siblings": [ + "12232255472757573282178506675896312779324531241126920041952328880364311510501", + "16733991162098192808933180539467182571007908216345347745634682222396617237609", + "1280912732546634306240755429475541380544236770831789846948704211269986486473", + "4765790185302443049742269279827183235276733623367862793222739954904205860811" + ] + } + } + ] + }, + { + "initial_trees_proof": { + "evals_proofs": [ + [ + [ + 13070757035139226279, + 982783479109927939, + 2123884927992108206, + 16236810652328349582, + 10494197717828776839, + 9448398560988197272, + 8011146453699744482, + 4092225454315853824, + 12599310637666180377, + 14142850848004064611, + 12656133716262824908, + 8376130194813593400, + 7359074565368594495, + 15045171678408401237, + 5686291021456044828, + 8455712747084933733, + 15056175555174274195, + 13669272686518709092, + 15326968674146462803, + 18182336872373519524, + 16476063286657483764, + 6072318591892209146, + 14957144708886171044, + 15666795893881829393, + 495292451319656295, + 6880639358021507510, + 6778124901986562008, + 8994520673171376320, + 7583982531391256007, + 15065290963509083627, + 61231511977144196, + 14880900961262918875, + 1907319478350035898, + 10527538717351865730, + 17250462730486958280, + 7493888587720753508, + 18053825582833841588, + 10866298626810378089, + 12380817267260283647, + 2351324852692038689, + 5650052068339093833, + 9042984598524544766, + 10650587506497954974, + 11009023976387889491, + 5458506171466754107, + 14535935367805550067, + 13473727931985197268, + 15016010214586147943, + 7870547668279151543, + 4723678687023210986, + 8013982546509913611, + 5399200707397839989, + 7808724880181489711, + 13982792684407386531, + 6696969806957095803, + 4964534185204782336, + 822193769636118095, + 6034276013874506113, + 14811520946709971490, + 771523042462212571, + 12775359293800736030, + 16718463721229452392, + 1896977386373825111, + 5497885829645173872, + 1323306295001273141, + 5698798505490816590, + 11698076883162487941, + 16958773838502673350, + 10332099164675140396, + 3334034266155645752, + 10278405247433592710, + 9772370042838847959, + 18036990190344101756, + 4431243494478240888, + 5329202612258741003, + 16437250651389120325, + 12317529791004990867, + 2024557859218991593, + 6091340599115372355, + 11918155707507907847, + 9509516882699084070, + 14526856962776005959, + 17230836008110645473, + 14223081887559107275, + 4161453297737841078, + 8364539367538128220 + ], + { + "siblings": [ + "464457822974894638213079451413728874452601304614690129340392940768990785622", + "9715748403313395164734020622503655652955548953746326896272401867332828653607", + "11764215951200983721956573736744833132076743853318520140249381700722836253813", + "4124428385895712148711832889437621449806708704266872993361348618593395399268", + "6242798098648236758976805149275900630094738292202836992054058373539392002236", + "18449803097580051594619980780685035991900338209255523592053908207175184693333", + "3192188753243113804689261365064049771805095956328589773099547413542325653400", + "15179233862413401958265993474864706791792113125891786484537259483301143124227", + "9640550749762083387589348346081407449354106190874074369307415603862563294667", + "4853060584885973451392770830022005791313093361438472866564781988587379406011", + "18026550184688394092931560844793005105443061141834785957534747761682293124727", + "8808092619865876568943873757207919964965518114424462894154004283305626150899" + ] + } + ], + [ + [ + 4820290149250410366, + 10820373795795410763, + 15645482225976987295, + 1893388199006755367, + 7566936626130676103, + 12362327706757301428, + 12790030965052904157, + 1102765647439860580, + 8995248100269481797, + 16516072841222011767, + 13569511765043122341, + 1113420175899281591, + 3226848538696554015, + 4925958764611384951, + 17773086089409381860, + 117989172411715800, + 1928655484749435033, + 10818848025328958995, + 7303766207789028240, + 3880516193145130729, + 13887922166370452963, + 14255077529232220424, + 8368337214344664430, + 10071766503214418981, + 4637422428469974603, + 12693939232399729946, + 9111508177473224380, + 14720746762332130006, + 7556625690913948517, + 495154397790083305, + 7313165538075365057, + 4460700649797488191, + 12263380257054765753, + 656929441648063158, + 6887653950933232542, + 10703266595993633784, + 11515378044051786898, + 4081090303421338893, + 17781979375620598292, + 17715342862482002716, + 13412179909467778918, + 10985284817894088783, + 1229983842261245387, + 17816441973863142720, + 9653789961226086162, + 850225456618991052, + 11795384109793357220, + 17463717280383388450, + 6741707840267745167, + 15992729365554923551, + 5657665515738159690, + 6437971152698438939, + 10302161944743301941, + 16597134306184483966, + 13845291969788208795, + 12104206420736485788, + 748706915412150796, + 14999229213875698996, + 16298210311220629766, + 16116022690791565985, + 4713122919785148054, + 10434559785321579828, + 7408781972276818872, + 1761689248872443282, + 3499736947548526733, + 9108628072847037636, + 10376814113615870790, + 15058362109647313421, + 7958254857280294124, + 1362692986056120406, + 5635977949602973113, + 7602349194622592314, + 9575896308337030752, + 2215936235616240919, + 12184817478084947888, + 16731380691430878914, + 1583369744204542088, + 5275662577791244685, + 16299960201120931634, + 16999561314173575622, + 17801236058264484010, + 2132465180688396623, + 7113230267234322929, + 12595712614625139632, + 8266373351558482938, + 558149740086823594, + 17900292764168748312, + 18059174590543729320, + 17808690536171415920, + 7579406403707775475, + 13694733242460697715, + 2199121658349944977, + 3190267909402048839, + 12268324493117383505, + 11391322556774598025, + 6780910684604447349, + 16721172930926542259, + 1241902935767707499, + 7786223667296319527, + 2626073546693415404, + 16050235639673975211, + 16366974754072129507, + 2647797785592353511, + 3918611524239922920, + 14838246872738538998, + 12045948440718985033, + 11100830683804475585, + 9153610597074481694, + 6977276684028240555, + 5044286396091608270, + 995891061179779121, + 14613186204193047751, + 1449781548260820722, + 336264888237377734, + 13781111367189639114, + 6327302274376226808, + 10837266138584402198, + 11531844823103805329, + 5043832460790891331, + 17684353739698129649, + 7114338533248635126, + 6768004589320594544, + 7212668453665984979, + 12462624494864356847, + 9777360766214385209, + 8981592830510426621, + 101062838042413129, + 4053316368231208728, + 11166921096399287724, + 14193495051927810021, + 1445505550723934320, + 7749938419251682622, + 16972482703204461480, + 8048208941843333034, + 16986180817801111960, + 15040127316892421347 + ], + { + "siblings": [ + "5452727905993758064952788729485620961900693759091043654535493842545253457519", + "19452002165606593071177779694187994506583028469710711105599051989961862888764", + "4438805860001780697146956519235392905635062579644875480313394212088674930354", + "10046942704354785515142690668384132045397965032428945646527747896687173967107", + "13478277731243214232064267391213076083695420401305632036306290325707609259479", + "18792677356337121344782042842861689627158511970373628174830645853943653810466", + "356514793124629844018201621649402667013657431123770605684136629959519401846", + "5724747371255204013685631525160383201161051712830005126160955864009522922909", + "4483717875150165477554739011835249448854837938893734042638791000069412627580", + "9123199120586522574585357847297742832069775512106866100145674763234570161596", + "18816595484614675359932325128902571377221131356036848218551078168189123162138", + "1998102658276433662264892799502015512145849695386111169487227505235902733795" + ] + } + ], + [ + [ + 5674400312329714898, + 5112936897850769038, + 17500128361031097157, + 8719650185603237933, + 11321131111754771271, + 8115958474861602521, + 8353868536132973770, + 13836589299575136257, + 15710051164014894018, + 9402350866188911645, + 7228531847652879392, + 3410316147306161492, + 13852518803748841043, + 11419798627574117842, + 9561636247812215177, + 18095738672369514787, + 2009355148517426730, + 13287582039582286342, + 145005219519773563, + 1903640915706171663 + ], + { + "siblings": [ + "4783706141660732299813489486019879425299433141233256941618159904706085456940", + "4121443144365517781603052390338021653849931708639496781312672302312516681212", + "4945991965923975349395135742043142893969737400425158688727807619183120963658", + "3558317363486846432689508601113499651929614437829147260754106830925122969062", + "6938048923448686446872871004198900556432670482947267737308484730375329460099", + "757861234093303224062034930248241892046154911659601600491069998745551424847", + "2702114328122634519300168909131749692683149931880260571278306335680431389050", + "14384303040272690686117125975591643461629497695600958364155918362366841458300", + "1535279559676411159042561350253336944573273802925611218420933097865405344497", + "16095936883626773839525960434328521645039715809278778540381484211167717511640", + "6975775331299706229973027039866786809574977659508598167240396041574664084303", + "18166315801780454673186719774155956373640715737638090489111590402838431444289" + ] + } + ], + [ + [ + 15744593321496503304, + 15803068473645384532, + 6532185147196881455, + 5650091332798956021, + 10195818704612580000, + 9786458192815262557, + 18292515015114145770, + 9175610357906794633, + 9912628069723388460, + 1079315002075093877, + 6440674431590507704, + 16621946991454163588, + 10477032991095607193, + 17450506935634233927, + 5915003596676205895, + 17249152877752540765 + ], + { + "siblings": [ + "10305995364233172304779647271051721081286963316014467763756560766257470415764", + "4362085884597046138022419409579200066040427525184051993810148379066765211277", + "10317917507304193036883710009773412647998930910609150192957915095747181251961", + "16830433074484513049487256040742092215943232157274621714200481376548165903192", + "2821486441326119729354629952702263243862488141181693591562465227449981379462", + "4785505089089424233127614975897961938382190897053147061664636182189280516397", + "978698895591436878786457167892251023145606380093855985579498614917918063569", + "9205958743570932824330922050699380883172739236272304605849890715609112273104", + "14311996487006749767455785130775218236368763249218672193744835282376228200749", + "16826190067160687862585195674458792666406672484043419901730726303607364598891", + "6281750628040293370664662711938862562280207318192463112779768107261726741334", + "20817810881385048455825782978372464151908370232529820769549915689281021813589" + ] + } + ] + ] + }, + "steps": [ + { + "evals": [ + [ + 13514790751094644746, + 17139807765753932584 + ], + [ + 8425664392068940823, + 12560270756560923229 + ], + [ + 17876134268900328078, + 4398727407121968456 + ], + [ + 2586599072952814779, + 14302076936692797567 + ], + [ + 15514991714489873822, + 4694762042403363069 + ], + [ + 11714413340999981895, + 1166117847862315972 + ], + [ + 15252125902365753967, + 17981655551430907226 + ], + [ + 92822228176891732, + 12994096631614102853 + ], + [ + 13498149200643818490, + 8690704524763767849 + ], + [ + 10676323450482926864, + 3152792202229672609 + ], + [ + 8801407721557643825, + 6551119378141229510 + ], + [ + 15942987957740569821, + 7870787010613140907 + ], + [ + 10455751966671215608, + 18134979581108486237 + ], + [ + 15694739077147255384, + 10380427865348586239 + ], + [ + 11871475020280812573, + 3200527164616589716 + ], + [ + 1558544896384403043, + 12993821999220737271 + ] + ], + "merkle_proof": { + "siblings": [ + "21310420978653243003836305789059698086045507142522903197426402467245219286881", + "372316429572271347734493269887893985095353214707253638058407984018321185342", + "3465643826908285743956832076028445577067536726929986134181079642422990490185", + "14949661827026745245766387353394986456103097633974526059752445725613761826151", + "5822395268433541280152587318996909444321452286554831191483570873890348458069", + "498341089623449998087144834522516061407648252342626895725756718156741356515", + "21113811989086646924549433938810745056387415995799336612475781911734830176691", + "18796407632366312126747469892256705122902328415187205982153258190665502119492" + ] + } + }, + { + "evals": [ + [ + 11488905745991257533, + 7564036809577766735 + ], + [ + 9330856623469530532, + 11262442774504246264 + ], + [ + 3412259541760656616, + 10149881874206186280 + ], + [ + 14076362821650368960, + 15840412507958253759 + ], + [ + 16332069699150718747, + 96008115830117342 + ], + [ + 3579025277871961786, + 903552590270316908 + ], + [ + 9605486846485472551, + 783918338338447896 + ], + [ + 10644664645442218692, + 16884335152701146070 + ], + [ + 2679891427125360449, + 12851489504800558604 + ], + [ + 16961325132374996722, + 9853761937500766458 + ], + [ + 8622700611361350043, + 1231709248335205974 + ], + [ + 3172337872733565214, + 14874539579698682752 + ], + [ + 13247292185506029032, + 5931923076493898630 + ], + [ + 1927219951917045763, + 16905753931898934685 + ], + [ + 14818797764797433799, + 5804802353101552581 + ], + [ + 11220191758889865495, + 4582909443224656875 + ] + ], + "merkle_proof": { + "siblings": [ + "8550463060280565059382833234391302489863484035833230003109662724155380506086", + "18508748882769305359415284312280093074972531004767156418573801441445507474651", + "13577769404177141572214918377809286329260439018515864222168898591667436076349", + "16772845521094640194655599631071575564211278483810508469817620136835607719090" + ] + } + } + ] + }, + { + "initial_trees_proof": { + "evals_proofs": [ + [ + [ + 1295891454243354625, + 13672869354368775651, + 727094020229702742, + 15886984972007394800, + 18284094730230207606, + 5307389528826409239, + 653656548404005513, + 7578408961743204431, + 15104350688860781356, + 972280046900514307, + 4793963644439418035, + 16695968445326422007, + 10987990627693021881, + 3658293852324306807, + 7720891170499861255, + 12247153874486732050, + 1953973523949571758, + 5175606319871236680, + 12640416445358258967, + 12088670369937452975, + 4021568201946060445, + 2722463622484608844, + 12729694082679718924, + 3606279323735594869, + 3924677088269871369, + 11293582800774773633, + 10290176233258691943, + 16259489362530216651, + 13005641457443792363, + 2252001419859952397, + 2838267591318768556, + 11171043503187745941, + 17145686941936099416, + 17755570500960335430, + 16455962940965621898, + 18246804900245553438, + 15183835046132291146, + 6868179239646725829, + 2830358814443030266, + 6088052316749786237, + 1685970344253264943, + 4340401564761831721, + 4397339585398476590, + 6155227575740384556, + 2090859995986984689, + 17798975761542163325, + 16052154068601182978, + 1064763937794465330, + 9666879324495070545, + 11831860217659866630, + 10026877937988436951, + 7661982736463542433, + 12805831982207196870, + 13828312960646349860, + 6054905441580978745, + 11070800808990915871, + 6823441362322154548, + 4986392696487226101, + 9857834124728805908, + 5784131274024001497, + 509230991602340144, + 10285540794785025921, + 10988220296115443497, + 7184633490343936626, + 5937200430482580823, + 3163824190183247646, + 16734966211635773367, + 10701918893731218480, + 5668723749238752227, + 5385835442462448488, + 1702167296117697057, + 8209381509640710708, + 337647078976251737, + 6277005424801159133, + 10993566539474642567, + 12777635540573868599, + 3047897277265255039, + 5959818360919827475, + 15728637653674656007, + 11658094073575386692, + 7554643365965084565, + 8577115883420605876, + 5239291463794287680, + 7269559722091786830, + 9930308701347210988, + 7996431779585611680 + ], + { + "siblings": [ + "950729130668939445204238342960838716179765542456064339009070425516615844846", + "16849607994781497403034286845346395766637573635615422387384487356878427696326", + "5462861204911259494548095304450504698710646831350753085915252289139291289648", + "8929681125394653794210992096298749736051564689854062654906898625273967023073", + "7688508791884557484351435527536873327159627498295536875756213419839948662482", + "2094321026262290913677292301000686560574483074314671961231012540396078981516", + "9630617086913405657707946209670088088886382532434932191430262671188345194213", + "12128134859681753282034302302157033523211163888613003021054372965537101432009", + "14113311104866975205544040767811262128150481267229509702841982169895400770284", + "13065675260089118323241680390458759451554516110324193190086927503949003859730", + "7569823242934143015163936757088083151770959118942968036622252786897345535272", + "10653550686596330216260189556975795724369167253562703920284250983981193623818" + ] + } + ], + [ + [ + 3678133047161227748, + 2981285198819670388, + 6994744246423599370, + 14398986067912748118, + 13811595767971725943, + 72174057288888574, + 9425746609428622419, + 7502857801045103796, + 8889198644192196561, + 2948797021452526473, + 4802871496564036558, + 5722797934789622886, + 15939368124770895945, + 6019031820660328104, + 2758820153081815993, + 8153192582784886803, + 9518080662518949238, + 16314137009315776019, + 4803087829664274062, + 9559592588444523418, + 15285959459288596053, + 4551177987955131875, + 7524866770321268475, + 17552230454266045369, + 1677369807463590830, + 3024330529040949676, + 9384421165217337035, + 204045412381376434, + 12411722142427446551, + 16768051499662444517, + 9932931794685039911, + 4647751434585985001, + 5405446041069067172, + 6010821270538792496, + 11442234257644327033, + 8284509970609349806, + 15213697440969410182, + 16395852964810880559, + 14409620138114223273, + 13595338020592563382, + 15274701077644617239, + 5531080378896171504, + 3097680000263889443, + 12884649763854215796, + 2168517608867049564, + 5022487735150533385, + 17497421898833947563, + 9874021724929456881, + 15778610165193580745, + 14126769062525444409, + 11239389859088703254, + 6680588423766943523, + 7822003078220747927, + 5079842412161508192, + 15243140052324091039, + 14603346300287732160, + 14124150815063443816, + 6599400560009420707, + 15030069817364570895, + 7030433775293309098, + 6751285363906762679, + 16909412236438188975, + 2588159007018653867, + 403304424162920162, + 14152727436229607421, + 7713384315979423938, + 5778390254200676590, + 235651452013335837, + 10511345430367880912, + 6715574662456232115, + 758305838172506973, + 3765586979681845035, + 82614744084856771, + 10012727822479532468, + 5228236076784563096, + 3427221158034318911, + 69527528313627521, + 4862958411247194344, + 1587242090032872376, + 14776046437050166429, + 8552068120403819192, + 11533706264648664417, + 16650628900168460080, + 12790354368486133501, + 5321861834154389753, + 16697060632955149378, + 9837101427366804318, + 3314843308465590543, + 4838612337112436427, + 9728862872093771162, + 17124420491499316079, + 14932980503659864498, + 15372352112421003065, + 9054123290333407355, + 9344140926017961905, + 845473596247776580, + 217731411672173813, + 11456442992504549879, + 16986827074048326915, + 505112686641966800, + 3511703915909683734, + 4467265021456785496, + 16067466102804162037, + 7352943069074011511, + 2129371309135610370, + 13777020672491929525, + 7847303871229134022, + 8390699189375644763, + 3509300470333850745, + 11652159826988897921, + 1529831210457162235, + 9354093515516153083, + 1954915425120642283, + 16159314530480186708, + 3193809717744564854, + 4673222814643611440, + 1834326340799940229, + 13327328812654400637, + 14261930647700192347, + 16394100619648618926, + 7430122178583838423, + 15821291695523155898, + 6710526826062212777, + 10982510715236905181, + 13594198970476408154, + 4209516508936094085, + 14193966930971207641, + 11090576478168448629, + 17455903536021195562, + 2391360096112414442, + 9354885571994928356, + 9268379939383051297, + 187017441239299605, + 15599652783620899792, + 5363926448555499741, + 6657164399205818900 + ], + { + "siblings": [ + "234495117077957858976604934452722449505250078220972084770169717953228905820", + "13655520657358680525639028395068729270210993306500746588297836840966402748473", + "3444679963418721298571321060159210052428398386017892291664646879798773990145", + "6727778375069313593030476711709312460551691681350118064852556922964923946235", + "5892593230205608465172795955601075155577475273465246444948745822927038366094", + "9611303735251251390238970614750022860926435556281576378397666651602596471938", + "7254161007069281635441786773260789356700468910810816005620188329710514282442", + "930736336238492077931980020573733520938215279834120979250295129008274077974", + "15432526987020532976909625400948166100530644928826297300942259645445370276086", + "5823242434159505894465312183828657986977367376190584916867358853830505023096", + "20299984174380995882023376328880561423004334070681899712030452907669913935044", + "17102734777140569498134893169723439669306318756105884790504740593163678870668" + ] + } + ], + [ + [ + 3765920783564968880, + 5887387556690700226, + 1140009195810310607, + 10010647446873682309, + 1188701131856829652, + 10990441138454967545, + 17075160126743864335, + 748088074355816015, + 4933302492396509603, + 16292810861639902228, + 208614537840000240, + 13134547880957183448, + 766544974426012039, + 15093781831558053374, + 4453137572845312, + 15086962971425160045, + 8985582545506860106, + 9422736659798276299, + 14579930715651976721, + 18154137399764358482 + ], + { + "siblings": [ + "307445013563772715882687804563483960247832508669672559147837037286953637176", + "9931018993111468366683054451823944307925177845044607485950777651241265647912", + "21643779881096501175783879227301603598549288989109962133834444139680792213552", + "19590786316506119264741068174428613373033691488139853434568355751826047456469", + "12521666536675819380493210739010717133015101931345729587473430066373578296833", + "12479171690376556949999390967884542881590336248175889750790911138932120490836", + "8181076583598692794665155361990574369399096634352032164870136872090306684101", + "1981317988374254728173581525975508838698530538822283446571613705384875892829", + "8501314631461318436548496252623175051683057959916049707169393772800527471608", + "20869164376036093879480625654812111199286733934118508249913468579659579234956", + "6106304131487426490291318796914473059908853918372508081425255615790281713433", + "12381953283542164394106057043905909805521116941643719107653870293686528453414" + ] + } + ], + [ + [ + 2687909377304226532, + 2683337840891893985, + 9661848081795469482, + 4257681282622788147, + 12484829127869510097, + 15368307321820376279, + 8738544532488869311, + 9709439765442557789, + 16232448208958349078, + 4347915034181291474, + 14406261049847627628, + 13197930740011938691, + 7883771622667731821, + 12409473205962852304, + 2338140571826324817, + 7279578239363209900 + ], + { + "siblings": [ + "16906787509957634139260526707708971795450241774628692914165382752392631405255", + "21783422080942901598487059750278875644927556249645613358554893072533691604642", + "6286256205274009010221433851720421690577989374266529951831725202213853452104", + "2597007702012338026960571303673133380108620440975213351056636476740717527272", + "12267288153590531108018390437673901465811968770609377463025736412398895388009", + "6887093820371117045532303894792143970298127052975880194039613754533852774360", + "2301044891597173153906767171301171011400424529529901793027609993043177015769", + "3351423526676516573651431638866359300753443156944437090931304973221584454746", + "3196954262411244521052410683722393322227628702968339425797807826819075512282", + "7026554037054653345723893528829456291167079373212404455992648308881079708866", + "20421609017148660284523228457861218285087720453212166044635655222958881066354", + "9278881599393559846283704430948983813265393216919979143989329616470805354689" + ] + } + ] + ] + }, + "steps": [ + { + "evals": [ + [ + 17518869500402841927, + 14412187933399986796 + ], + [ + 12795511940333324603, + 6075692405724275340 + ], + [ + 5874967145466961657, + 12699799385428884364 + ], + [ + 14978789284669635567, + 6725893950524141209 + ], + [ + 7544901632574682916, + 2479619164409825190 + ], + [ + 10961757921092896579, + 9676354691997083114 + ], + [ + 1433889195454835691, + 7672180038017365026 + ], + [ + 9946251756923991301, + 728450164022905714 + ], + [ + 16646443120358462998, + 7989403230617690844 + ], + [ + 15574737332365450357, + 12078182093704532514 + ], + [ + 3938076753693578708, + 6216961718123539188 + ], + [ + 7185674475535924627, + 289856433919244392 + ], + [ + 9145308099672768628, + 4629362088901565546 + ], + [ + 956334820131870609, + 2216401206513634786 + ], + [ + 698490785829224786, + 12637008783882300125 + ], + [ + 17035269357957658401, + 12749083453980045997 + ] + ], + "merkle_proof": { + "siblings": [ + "3870718618218574862089367368838939591407235283230394410442717417548976247764", + "1823399558388363125006699888606981368128057346547818277886120732805455691925", + "12462885491676979425922855482212909001546836927506254001912860865386976287316", + "11947078237130265516063870756056560208058732570316702539536713631815329061885", + "1830202855717260432222978735524713372679153435885986177031005000582694319316", + "16521709322288096688854080635608131227104844946963286624970719905327641967802", + "19160817325325509699862405439630873561742184727802710177914858610737505515435", + "4383963644479008782800033420830194228071156195294500682032982382678282922575" + ] + } + }, + { + "evals": [ + [ + 10596966911662752433, + 4862403481034732652 + ], + [ + 14493073370996915034, + 15504495018941935402 + ], + [ + 12660779992508821044, + 18135502278146962511 + ], + [ + 3747377331714647719, + 9956441548529175864 + ], + [ + 2180257330088905134, + 16843280360301817207 + ], + [ + 4983460306479997479, + 12277641835267819988 + ], + [ + 2438085387962701394, + 8383070014396230818 + ], + [ + 11509959294136398507, + 2419038699703781215 + ], + [ + 13085641933897990143, + 12838885205917872282 + ], + [ + 11018823771965019724, + 17922469043860335177 + ], + [ + 1418238310381363762, + 17738067182278994379 + ], + [ + 16861009132571445773, + 6185187407536283361 + ], + [ + 17114250185520230813, + 4176018661519660393 + ], + [ + 8087611362155158749, + 7057310186723238127 + ], + [ + 1357489721363363528, + 8359860138134403299 + ], + [ + 3733099526712108674, + 17300836341087993412 + ] + ], + "merkle_proof": { + "siblings": [ + "1675158065499957734439042700458989355319955257401902168901596979126480173008", + "529066789969314922246252694411698070524030669954913896944182093820143070700", + "9905469789395796226438335789589920869443139898236672864326806306588795816641", + "10584290545658388272113831917559430943419487413072249847345799244410385894806" + ] + } + } + ] + }, + { + "initial_trees_proof": { + "evals_proofs": [ + [ + [ + 7938984587855847790, + 10354577192474017471, + 5390916459596209031, + 4470243362888225798, + 17785817007935753211, + 14001903238350627215, + 12357794025458741960, + 11559199196209907061, + 9125351629085744530, + 1375879411119283097, + 15584050819913400113, + 9395225368711317374, + 13088998022676021984, + 6578094134182861750, + 16900602249097349346, + 6469676504091083089, + 226603536581568051, + 11701701134258972016, + 5388408662620610214, + 15484627099577867852, + 9357416981344225522, + 1357799864241145264, + 9241476037894143567, + 2339624195804845685, + 2536244420067426752, + 16042617734679101214, + 3539287913326513510, + 12869313628228505515, + 15002193588625243265, + 11752517954751780321, + 13840860880425378129, + 16490584817576878245, + 769124011704417360, + 1005261515993868596, + 3221491231244148230, + 12697920779348264697, + 7787057288048408375, + 15813116302779036855, + 6558320644013737864, + 10194043000131798749, + 14112103696621712799, + 18354944090549008359, + 4902378550221504621, + 792791349328417755, + 15376884536466506314, + 4130412771570397926, + 15216274917586225539, + 6574364457878601746, + 10116086796226859617, + 3711027658808335929, + 17448392471876486608, + 15290828882905922092, + 4076591693480356596, + 4537424826986665562, + 9723136107681251336, + 12070219472664167506, + 7336348651038933097, + 14224338721975368017, + 3911371400640349329, + 6087418679274939153, + 7783045263523713998, + 2776763350967583018, + 16399166720096682484, + 12856532407481697724, + 4858218978004191386, + 696612460441064351, + 15674740032900665727, + 16720238937819293496, + 11471144066586539958, + 5546335889804667705, + 10520466574010602131, + 11487608104434338030, + 7139883122149948395, + 17661863660040137797, + 16432542159435008602, + 9573484074610844411, + 13531540924514832016, + 10175425350992776520, + 13621888155785451302, + 11385196335460603071, + 4934675121779007111, + 6850020189410812769, + 14082775938873620691, + 2470359717322518335, + 13705279927093280719, + 14962701024847342703 + ], + { + "siblings": [ + "19059597135603760435090836783806061317763085332262750826040328820494204131889", + "14860276086673899326839299291667529616555045028398606697234296892597299654414", + "2485018689987596543232648037864984400834252082574681845156513617799246002552", + "6949328353070239011803055076933910841970893532702278791995772450110407157877", + "10985871584827308904599275678038211758324912790383000802369103944601821281042", + "17435031773258960798670115399747344740892509317714653472936549400164670337975", + "4839408189287104416707967486960358025592395591020470704719442830242648745584", + "20428371237017092755889519831661134344430231760483881707164040790659126753764", + "16779294104451377322736161540427355882206467873913872415989707525490670043228", + "8124944102154344740248193124715500524118558167911155008193347514993262841611", + "7542733679750042350873185962536546355747607965109942451893507300540124898945", + "4338138459904498838829422008175702150897266294558914295460682045025061764120" + ] + } + ], + [ + [ + 4252068096673651979, + 11678384869529618798, + 15199680166001418594, + 16403367834240641707, + 10686394570025935345, + 8929103172726956650, + 14517148551104495627, + 966421712247527781, + 4549488001552154133, + 6129414763483366996, + 16118207678700742975, + 3253998280335040997, + 10124901183218147968, + 3258906196735506787, + 18425859784521390466, + 10844429452148655770, + 11632811601726448082, + 2543572816498379734, + 2598179800940536278, + 9375443410576273358, + 18060603690480127142, + 874263852704318500, + 17920578275566830952, + 17074865076394004400, + 15990958316864912497, + 9814655322909181312, + 6724240401845673238, + 16996868253023689116, + 1104395935369878149, + 14893488858272519093, + 14715881856354735558, + 11991508404475459226, + 15607483780472918321, + 9576491078744931971, + 2253781468792408536, + 17161046072953771677, + 9440473341118963025, + 17004011705967077541, + 12682579059410527012, + 1000648358682667620, + 7406735185774537770, + 16975153593748863376, + 111470633048276606, + 7580612390514391364, + 1860362015797889559, + 3202364617915789914, + 17021192729518976524, + 14717271128457790392, + 890587031243522494, + 16819231971335711029, + 18084158532092572230, + 12395860815343213265, + 15599300822575975173, + 10458076352389590605, + 8930169074186039627, + 8314831542607671061, + 3366078255934344642, + 7286392862959271800, + 4513385798508193633, + 15559849667157592263, + 17413727400629424544, + 4113334515378440851, + 8321616842491386775, + 15063658860766139510, + 17882252792341220875, + 7276996581094628616, + 5870151564393362945, + 17564346374944016724, + 12690704238149131474, + 11504224615012387555, + 11272426131532066592, + 432689076416748625, + 17480778239307385626, + 4547017645708061896, + 6861274506897902266, + 1992861900353288220, + 1577770247819997567, + 3613236155239551991, + 3664192684212613716, + 9742162695631581549, + 12049083121610369434, + 7445851420520366643, + 4021421123241337713, + 10087589953960384244, + 16569354650495219300, + 15092094484557384922, + 11676470014193453106, + 13296162613826267262, + 11189774271972492422, + 9214051228613590731, + 2887194387183947601, + 2791322579981713651, + 1357391841971310234, + 5095479203112528895, + 724992092603650122, + 8942119958324359548, + 12253115791181166998, + 368153585402394240, + 5585562431759952807, + 10671997542564009117, + 5891664521230006336, + 5957602412569085627, + 11282268384307499232, + 17684398895949396599, + 5233158202096617139, + 7082004169403673164, + 13059839095556054815, + 12748705567309431709, + 10068680669329020953, + 5959758649165961529, + 16960871544755415148, + 10570898124440450764, + 10742253627182762175, + 11285587325604758446, + 4747277208745393928, + 2878840211967363901, + 2957411801762712321, + 11856451197760452476, + 11361336691205591490, + 8944407674592091978, + 11386141196654773550, + 5284837302219015480, + 16530206174196380436, + 12596478179047823888, + 14946357984956131538, + 1731984257165482623, + 2689856915171156955, + 2458998804114839733, + 13138901097856853938, + 8602473539082028018, + 586708982724747384, + 479594575006936188, + 6773334167621344834, + 14797207818386570125, + 8247889628428654985, + 2888535792056589683 + ], + { + "siblings": [ + "21806741172481478703698445174271873135108001572864609813516313149609393681999", + "12462740810526493606926036778071370040272080970096299937256461919768952835633", + "8139215360852501066064506760901086045206124838619319803301186292664871249122", + "17391537839007950590551413646403171841580296808022694724827598346668023062796", + "1294296860078269269762289112226283376463717846784266295839609821036107975710", + "5276546872585049433292340591645812597569646156473932758571481794666015288369", + "18982686624691838910305438315447828037527588895275044986553085453224720346302", + "3558708417089379925408960692623589430060146326990883243863432319016110668533", + "20079003236433680230072442661391011646428557234593865580733479375919905312574", + "10323672413478293369688799336777475736519583853852636079948124519033738916961", + "17508498222524732326844698032355580013493382825223573308992106836058734575565", + "19470843374989056213758360445245008216293432390496275100463629006589451335953" + ] + } + ], + [ + [ + 2992299402879061018, + 18439746655779343787, + 8777774560103331616, + 16028381527728911989, + 6565286351034515699, + 1765369557468474982, + 1998866545248575529, + 11921105242266313461, + 12463731555092324010, + 13660245318403673440, + 9513774312241921510, + 1203602843263081492, + 9759825784971831066, + 4934746820573212950, + 7330635905294156860, + 17001539835999337922, + 5066694459256831615, + 2174081643953346349, + 5555984463575864710, + 7500383432778124351 + ], + { + "siblings": [ + "11734371721371432460953240438591732302017481514041244615077233353155135343270", + "10631343440726597667440404621582868685512802231271266717892105465126422981500", + "15691715417891139094946002365893432284165884056300064769684563105242564576432", + "1170651427236508993010316361714013383145805020497678476501390737839507685065", + "8687863412371131184588977758737959833475753107365610596802788132130447937102", + "18673785057331822324681491002761857422602514098406846369869132073897918755554", + "4157687667377378854649629581984393960733299140707308840892582953072213303143", + "6331798274413287237608714349495032783392875299330334250357470618739734298421", + "21455739655813669767207346849000331139075304218237120752787473045142155331704", + "11311648485825422048640215849245079730193751715266930481244827718190879223156", + "19875568667942931476648252286996835745212268718746384100065823078216157666343", + "7301677937739100135739096187669673915927995181456028847919102019794716132115" + ] + } + ], + [ + [ + 3485295662593568435, + 17509346962584849465, + 996315085545430181, + 18096547156295682971, + 10621039105458264366, + 922259532992617819, + 15634125155857013496, + 4924753789278665447, + 15881193830783802407, + 14229800410702547186, + 1497675092497474580, + 7499723323296891240, + 13596075660063072417, + 11768013629121328635, + 7548388656364103101, + 9913278888705884159 + ], + { + "siblings": [ + "17071578038221343516629277695876074448427979779656473531130902035131200185828", + "2804274995709388639248743355729316639784051029145651816764835698157451752334", + "116753066753783466884168873741807233962242410098145914504919010638577476923", + "991426661251505418585654676636533765789368307319384100678409162621375495733", + "11643118288593854814829526839348330170009644875920584959141866673022990075912", + "15936531823172606316319585947775255649456737433453241793435100166057473410105", + "16797716103845217256567611581308356974941117932198646924126623928067302037858", + "7988074321053622355739289400538787253578070902667554822813197083694976321463", + "19525726013382353844991567412470285079833858367633492110565235140677861367510", + "9695525605842972673692022231427146295624020375702833990503081148407501765689", + "7956498953999337947251901555444434026528156940676785105727935728368357551525", + "3699559523277873323569920790115140202910469643892443275995436654476776909911" + ] + } + ] + ] + }, + "steps": [ + { + "evals": [ + [ + 13291688176580849563, + 2670639783523753972 + ], + [ + 16941008233650605381, + 14909854395469560028 + ], + [ + 10604294647503922472, + 11994637376196770137 + ], + [ + 6078011949729379456, + 11459271687886313542 + ], + [ + 4154264871905738202, + 15996728600054306166 + ], + [ + 11852121756528677863, + 5257780698562781941 + ], + [ + 17900142921030224298, + 6354959930614498434 + ], + [ + 12591473922513517931, + 15498465786959998168 + ], + [ + 9041088200856875503, + 4600513138568901445 + ], + [ + 15972920622152512938, + 1393889463377468649 + ], + [ + 4708375275702495531, + 1795265824552452835 + ], + [ + 13900107230303285554, + 8331585016913171693 + ], + [ + 11444852325868331396, + 543894330378381158 + ], + [ + 5049540580305548496, + 14477391850025078984 + ], + [ + 18234250294972080922, + 7118574542249756461 + ], + [ + 1056437134177471510, + 11511013298732521691 + ] + ], + "merkle_proof": { + "siblings": [ + "7037591630811359754575024269282385189490718330552667508327738232043032718454", + "19766237811050479459002243721353878134548832828795564261579148911761782398550", + "10195649581741806280771387270359168363135114644780348915483579351442638164439", + "16322861952914106687039400136575991982992525208918763317318177802266126692279", + "13359115719067333210281014983545890700909214414557364706081436090562802468619", + "8072467754980642668541155653040191567390527524976290799938756242195044259948", + "5385468674422905087185223527515607599741615039339654110106927283022597760991", + "7784947157310184095674313826782217080394599903964448541635919537567075327554" + ] + } + }, + { + "evals": [ + [ + 69703946557929957, + 6873952681616078157 + ], + [ + 16176560661713696751, + 3779182932773952154 + ], + [ + 8014174143313076606, + 5988218640387098892 + ], + [ + 3523603352745571284, + 15496005340257584592 + ], + [ + 3748738075613153801, + 11730728621557298706 + ], + [ + 17313056481411688330, + 3409666309218695015 + ], + [ + 698330977274707779, + 3494557296683794700 + ], + [ + 13240433543478525466, + 12240984172455535689 + ], + [ + 5231411598014165670, + 14041841602431829983 + ], + [ + 16388734943089858615, + 11078700813017056986 + ], + [ + 7220543047750857659, + 9099997317831300003 + ], + [ + 7824180835264798092, + 6841644888500817240 + ], + [ + 15538107057683850595, + 16358832204854960981 + ], + [ + 2275440366792793600, + 14388495655531875932 + ], + [ + 15177961382170124505, + 274015561596604555 + ], + [ + 15285831656119391657, + 15985317306214366251 + ] + ], + "merkle_proof": { + "siblings": [ + "4634633570285723166943017303518344586245275132302592417001359077574526700762", + "16783920940527945076215781695988693921884379318957447082474851928169869960776", + "13776249969088759158481983632327839657450625791476960026604633014893896974705", + "8484183348157293902862836087362508824383218680737312619243950900953774854769" + ] + } + } + ] + }, + { + "initial_trees_proof": { + "evals_proofs": [ + [ + [ + 6558254195776388694, + 6876819087645301875, + 13047752276134367384, + 15959570098644820405, + 18072917563128111543, + 514049073904739597, + 12231041446829620412, + 4914269672274297666, + 2081743466779196833, + 7898766726046929764, + 10037326198430881934, + 8003121914568133455, + 2829905938906348303, + 1296363618264211619, + 14786368281020009584, + 17783088309595825504, + 8043570660310848954, + 12280632385697475537, + 13833739586108308882, + 10474343593059681006, + 14758508915728447656, + 14023723159305356339, + 670328574931293379, + 11961025688681160125, + 15909542571183470931, + 4357661898886214270, + 7337720978224875259, + 7140829745549516229, + 4950080449533796607, + 273106315114786115, + 16227029399431951669, + 3946042457912588013, + 10855671262270393518, + 4114206949268511237, + 16454194271960853955, + 8004997879424327377, + 4247658565388616913, + 1527684416733703798, + 9185722456122678813, + 5987754214404379320, + 9689807580375112231, + 3495752820645041345, + 17592976728807668020, + 7598826309946489490, + 6247410329870181784, + 6408339058796952544, + 8177910118124778830, + 9048459079725297153, + 10376809748400630290, + 13179034772525580680, + 15042244802758753048, + 1650914008328101809, + 14702757333674456470, + 9367741209381719498, + 17001389710065269546, + 9982587723554700178, + 7389231690934350711, + 17723915792190379452, + 699047667626049839, + 5800213705905982106, + 16203971492582146322, + 9773891664475499320, + 6457206150004172356, + 1321737228375626652, + 16957855404747109931, + 12774279699586084053, + 15140414294992482392, + 7552108473365215746, + 5466161058763001838, + 5454395087179201537, + 8644413502732129160, + 1506864351115898640, + 10150106469748233706, + 13725816600710176260, + 15606720357723197562, + 13832131530593800876, + 10325514971743981619, + 13883361084505037368, + 1327775538580831511, + 2232451091547731122, + 12779092618327444777, + 18215538533675061067, + 10850565518022219370, + 2317186631706915265, + 3761702284505120789, + 4278506476929997033 + ], + { + "siblings": [ + "2287835229358995042900894603749749192845305105309501937425239707055028389477", + "16021852611101928495404046899921830742198315850355439249613120445333356273859", + "10657710928940319610283472259061231499899313644448826450154340125091937959035", + "16859401625240280720491163079186097073129243814035261014652754634476193156305", + "17656696720294544327776906007093129628580252688994161605538342297854983701381", + "2200077471574160374800358852642818391033573726023880189544657248747072221282", + "4388811414579492598729814348407337338975179593448587021808600761959607979611", + "11672875664448765341690633810723588992953724409008854911634485026387117141483", + "5073540842684656902236207975480650620669036794328934793589311346546237934443", + "2461265452755091327076813876173428719267704124623927280927314681085338119661", + "6321900665243986348280019422281627732246640968101709693294539901747022763725", + "14977980896891500164175508978422692325928989322015707229730562255894221180430" + ] + } + ], + [ + [ + 17093669026184407755, + 1355130772501476569, + 4841583268771618098, + 13792031032592486306, + 12698082465105263355, + 4295892150443517277, + 2460123136517027640, + 7222698851462564666, + 11039586281295807006, + 838414183181111543, + 1463205948139122001, + 3393131477488526042, + 7601075322138541487, + 13459491758745004071, + 10163037472068847087, + 13804924200102348946, + 6899201870697840455, + 14072285425765165569, + 14899606312427123356, + 1975602195873143904, + 12809554934575677893, + 10373181851400664799, + 10759879409038674130, + 18413624731370998789, + 17750770192316291097, + 5720341502210064472, + 10953797218954247552, + 18254403500219241024, + 4241345416602043053, + 6643365815886896223, + 4221101147988367073, + 2240245624339119810, + 4840444972658846747, + 2030142060985658938, + 4321942984600742710, + 9055512571967813558, + 15565198692905695129, + 18144884873248019043, + 9244702291780467922, + 3611905407433056220, + 9807073925022152595, + 10024522259374196199, + 1029534408265799287, + 14023821655087073844, + 10401020985001227580, + 10801435786526585083, + 15573646678638817528, + 3002017347589915277, + 15138450395670166100, + 15081764630983418885, + 2827922136834048967, + 442984129719965537, + 10472149315871433812, + 8266036474616625837, + 3253421560140094224, + 4092470200241016011, + 7400682311552584061, + 3156385418351056033, + 12380675890309253419, + 14396269415697925528, + 15119633024617620501, + 15621056341349147973, + 108750459330530872, + 2346043696002915714, + 8833583352123922900, + 10285656423944181994, + 3935691681048145389, + 7089515916039165455, + 16280844653975233702, + 17998756676849965783, + 10968406333115364102, + 9832610636051728207, + 1329176628864315995, + 601541999623254288, + 5562151462279972245, + 1921580614728106131, + 179508032323849735, + 11494249870273885592, + 470726594518850075, + 4037098761159888075, + 14076050069522006947, + 10121737949935924005, + 16065553371470492174, + 16026768962646890530, + 9751879926446594613, + 5977318046878463390, + 17306651949144843125, + 3457174843995297549, + 9873398135076257645, + 17384642334618967232, + 1217734517745921506, + 4496646271809672968, + 13713285787318277860, + 13138391535249592375, + 6575167186973588704, + 17336733913289636233, + 5427463100868563624, + 6407182115897554907, + 10160966814670609984, + 28346402919555079, + 94490840580858244, + 12554559251646700740, + 6860126756264319754, + 9794636015444518794, + 4475987207094991426, + 9632974797165825532, + 4788729892748381899, + 4756077060998597489, + 15515800893240929716, + 12383966361757151432, + 13995564397165483464, + 14592171934715919271, + 16015415359351597093, + 13988983524267749389, + 1887376556928192768, + 13596060888083023694, + 11824877739798249389, + 18262355496432779257, + 3585540415817908857, + 16486954240872878786, + 373502603110853668, + 6711328865959255014, + 5129007875630515579, + 7532963436909900816, + 8181912002484027457, + 18310206957185022971, + 12759555269975400029, + 14040821541753491268, + 1050504772040147062, + 5670763624461144572, + 5276173863014836862, + 3927582583093707063, + 8939009517429301570, + 8592858492415019902, + 18174254039963920122, + 2043422306210822253 + ], + { + "siblings": [ + "13280839983701904095037125508446272861236899569602136156166287208362120144940", + "4908641040647433861421435140158471091813931299711733206203581113871130913608", + "16688912724755890870400375073385211021807440864773732527370625588309695787862", + "6456410162232895752405275409275312619437141081554713303219931399602345436597", + "3197001808944920006000059266131024952282544350834130779086972625369920141406", + "9585634441622127617600564553227971746294162593975232200701044453808523149646", + "14885605691023265670272757511594250970209758478003090969507417076569356158493", + "19830728159655350248715939556687122755685408303600234647834673747531786553607", + "611803154500573730198827267194431425530961893306515257585273170599122654951", + "3559169839479773825186549324458841577976852424812892373421734133689770562269", + "8606121530062924320010372070343645470026910876695854753775321705644775197507", + "17792072638948763536500924504698332092626147844783714620673728193880298349869" + ] + } + ], + [ + [ + 15747940025473185670, + 950635745359304108, + 11708011257570548391, + 16739686691099202749, + 11979943442019201810, + 12237637057769200756, + 12336104945927187659, + 17183661766230509037, + 7995030503331593637, + 5772729383749859128, + 7019275637325740480, + 5584343692898356267, + 6703753172531053017, + 17753637725836067856, + 14004781884319444388, + 3144391203888332192, + 14432265838205951310, + 17975811655200371556, + 9743979689324785856, + 5046224709767154170 + ], + { + "siblings": [ + "21423907425580100504912950193545256109146319080695940833332531537247213085639", + "1804736992878267514652321167661218910221569787202496991140666906930360727500", + "14404414456893104725542623066231217332619741455584095731451450569610641286996", + "12876631342113713898534342969446913780082842213497977730576527325551110299751", + "12957235871564210114855353290758812497945896014640667055080430410286818562035", + "7200938390406583683528089198221684226744610584396480366392765044488658351981", + "18411876304862203236363908406677865914639020395458037479380602579783464716322", + "5548167077825080281466768437434083191109900069279002476236344530972205982904", + "21097578454238547125557431180671419962929807680134935026366942864526711609712", + "16647936273106473880420181345205171201393875442040352623837053969165843010181", + "20363185475925668766156127008146068952749869367190797542017309233088813047072", + "20121433522723199745602190842834615995352426038686657778624068854909581759383" + ] + } + ], + [ + [ + 4189977542388682930, + 11592137927719135763, + 10263008634577494082, + 9459204929332425511, + 1882041422357130967, + 2095417952069819615, + 17120115019947321348, + 9928242440684987857, + 1408197140266189238, + 762277764751238843, + 5992218241631579813, + 10090667511870601212, + 17050841906801595930, + 3728932681047060930, + 3739295226317749688, + 13784579717042771449 + ], + { + "siblings": [ + "10535084859537621427984950771853021319950434339040274866832386324143814916427", + "12073195066028095049028364423427603200929109190107717018923812497377031721768", + "7440741104269024735513773804817062353592152117271259390446252902282376486672", + "11922604643321206081329655661534802173701142673544902477440522535105731720167", + "20638700568672696762686379192828028967664761428319746551184275579828356142538", + "15602763577336483563418489501442661418335387074727991590813403384369136907770", + "307749287441856753723079989442760917564743413576220632713693930095845326230", + "10015070914916071177635290438964410714702709706634963723162189768953608089348", + "18721014558492488813981594387260226054979402325204460523507877751478210879936", + "18654628391091064291054376138559603144337458338983934976481241090622327698108", + "6017069121878336662182306765601655647157743552584406684548690122085412810214", + "10637911846442861130245832374410620852556625420628394127797146596771726162242" + ] + } + ] + ] + }, + "steps": [ + { + "evals": [ + [ + 507364308273268417, + 7170877971608722433 + ], + [ + 5740116631049216075, + 17160837402348482612 + ], + [ + 14161497148135733584, + 13058274118552819361 + ], + [ + 16428943694842345074, + 12771140542341076363 + ], + [ + 1765881336630317299, + 9136848603689641717 + ], + [ + 15769393225054376489, + 15557796840161575722 + ], + [ + 6101803517643815167, + 9970656292292954727 + ], + [ + 5825508014390784074, + 316183960985682159 + ], + [ + 5645502227815056944, + 12562059506624952140 + ], + [ + 1506333789127531955, + 6606600787767988058 + ], + [ + 16269783671516645020, + 17657833758099417537 + ], + [ + 8847687354179726863, + 15248540252979365962 + ], + [ + 4302273333131820964, + 4184449056583925184 + ], + [ + 15421853767764183465, + 12849278436281114390 + ], + [ + 11555775951572017296, + 10207501943173658326 + ], + [ + 14901087258719147126, + 7336628370273328557 + ] + ], + "merkle_proof": { + "siblings": [ + "16008938393773574867908491937764036976577209761063127719942660992153090787994", + "15147933494304554963212785548159204969977225703608106194630966566149920000914", + "15766739163497885366850827717925779128927251122306020765606258158842519077508", + "3339115119733422909273558628451957636050334830838903401785845081621561135785", + "18029017702925043923463979761252710891484564478621525863401433695978439385980", + "18916381340145380605253992870079383686404818223129411691734284883997644086830", + "16981093979634775832023243723309754306457016082930507563702119473688576566065", + "13197048586821733592460454253830833232487098057843067486805048539662222718243" + ] + } + }, + { + "evals": [ + [ + 13411691955535232747, + 5050414602323150656 + ], + [ + 4020157059012937412, + 664758774058513662 + ], + [ + 7844807448030944882, + 16117453977952423598 + ], + [ + 17990233125909642202, + 2102505244824518030 + ], + [ + 10729712144598274362, + 18054094671540461481 + ], + [ + 8273297279053913058, + 18331342405865147536 + ], + [ + 1769117037191072785, + 1587642172972562244 + ], + [ + 7831426539022206157, + 9234362997700456814 + ], + [ + 6476010097312159887, + 3415203936896697892 + ], + [ + 13197302688696018627, + 13394945967000675930 + ], + [ + 2903530877602721907, + 5316932514464473430 + ], + [ + 10735746257742765439, + 15140283016889882491 + ], + [ + 7983486582692118417, + 11121890581922000573 + ], + [ + 14771577658777271512, + 13248004327173634194 + ], + [ + 1318902642363293891, + 14830139251666476853 + ], + [ + 11473704094180311897, + 11008045284570015386 + ] + ], + "merkle_proof": { + "siblings": [ + "17022814216788623294490329936555652512714720067429171879229464780572329541442", + "15646141987533325907234355604541696597691259101322376966453598208655453345976", + "20486449519169811007795979754687153763777827134389529818394772689254480666030", + "10641035367414985779046394614294878985796741424743753082367791021457764722350" + ] + } + } + ] + }, + { + "initial_trees_proof": { + "evals_proofs": [ + [ + [ + 13302645558419094747, + 16968278484183287786, + 9784850107063267464, + 15474546961204983830, + 10248826852570515536, + 8122760677460065403, + 2394573941152709420, + 16394082650902888532, + 14279596383056534666, + 7915116954248081356, + 11597222671304205682, + 15207393593757882418, + 7297628661710360768, + 13680869685153571408, + 11581599103041690013, + 15872740476193077854, + 1874638175734231789, + 18292116394159739884, + 2497340318965073470, + 6159936176736596034, + 537364591088643070, + 15131327861109486442, + 11227290103112475247, + 3568510922855902046, + 12910381289282705502, + 513558097201049483, + 827058045431685076, + 11677647978076304946, + 6483148455165940528, + 9646983589284031519, + 14395671491074777263, + 17483344341542140290, + 14887671112411539211, + 941852000138476705, + 5149213668378106902, + 207867497324723612, + 12264893459570295522, + 16877419596281815260, + 17288476900951654355, + 15473582505742595159, + 116101909007025928, + 3516135329678195529, + 16546759164289489596, + 9594800243433536030, + 15681451495873580132, + 7446130804393381415, + 5337231547944588775, + 17377603766411816465, + 4316614674026637126, + 7963440554009752443, + 12283761462267547829, + 16651674566140417813, + 9183564850608088046, + 9243877103327562759, + 9239214625967074485, + 6984441821625633679, + 11452771761005468508, + 8737028828014935182, + 5194123440853783609, + 2245110182202050742, + 10388337611381211766, + 4033173519051391395, + 10933134825418974204, + 16484749648637402677, + 5394147046227813771, + 10526252466565554226, + 1231743968582689319, + 13680075990879820860, + 163821420183325140, + 16806579152056411049, + 8714291519075608940, + 2166060215583928372, + 5867936660445405636, + 10000904967369748944, + 18163136970368095868, + 54957088430549490, + 16975004961373007195, + 2235770986214720719, + 6019922014474756022, + 1196172886619738014, + 6535217887815190794, + 3274004362829729876, + 9506048960735132984, + 1672907016084326752, + 9897379098914043762, + 1261443241031498201 + ], + { + "siblings": [ + "2725499247026329598016941509154434126591035198930985386724285257449543857936", + "19252901212800844040022234306408112080352250649649304972652779009530030969623", + "2659827589643848820605013480777471908007753892818725595397008567773321172030", + "4089650302333995150813946225407176659620124117871627835193300455248522543138", + "20166333462542927747023870984352309646360571001204689597771787939346512327116", + "8445491954231719241497923615811457600314781427938055990652034566843731638096", + "4336835774134748796560950294446508839774871518084426486341095921119480417254", + "21794439726773530931128005985751568146870236384856280682443201700075872572737", + "17157620011652329527719923994563197863376183445229189474791057942863050337385", + "6234171689816167762644001567559454206290105149644974101892010285050049288451", + "11962653073928804034288156006318453020283356565438547908128389439147802432972", + "20531359950793996073502242051998064322835724127990541525578136833693167734923" + ] + } + ], + [ + [ + 2467433412344499279, + 11266976777227087239, + 14849079288364932920, + 12471175335519960127, + 1052557560024266154, + 3012124075369002697, + 235397509069791984, + 13854189931052147618, + 7206460665114765573, + 4751251459065913695, + 11324678812107907772, + 258640154216954452, + 15318542705428913429, + 13838091500868172795, + 7962062126244497737, + 16035390055281046525, + 11386571279315572474, + 9358546457960895804, + 16197776346039234110, + 17053136203013979678, + 2804317955369943170, + 9025886431553740549, + 10202170667569926730, + 7986000238324142549, + 17328231636217097593, + 4412031343810837686, + 13379253956263962635, + 18063758943429992701, + 11245497200907118473, + 14908451166087391615, + 13785980106698941959, + 17756996223780877111, + 13918773891534190377, + 9006908685708504304, + 8278879238093800965, + 2017457094997739312, + 17444413050178502791, + 14363985058650880049, + 8191855246333196372, + 13735705980179767790, + 2398833671808950527, + 17587284672477888264, + 8274270521744168764, + 5731523952940064622, + 16568849290476684801, + 1454149021812830554, + 17450271646230073081, + 16449328328393839764, + 13118608351200601852, + 16436940773041953426, + 3758555228296254325, + 2556391727922586491, + 2593016762959019691, + 2916858915218721878, + 13293486833698388974, + 10740833862038161194, + 2112957902092677105, + 7821494702306385414, + 12152054146251806251, + 5140023469101078659, + 12635550398025993576, + 12769015001246867009, + 4539728351677002257, + 6046754161549359147, + 13816925610547512947, + 7068836248966186225, + 16738995702331295299, + 11555154470466352530, + 16933417716565285208, + 13529564519485184973, + 7538108352287364801, + 13238085845791243371, + 2250688446731581461, + 2107941986882106418, + 18166068049318919766, + 7327008533786589147, + 12996507162786371031, + 12676654072787020197, + 15611156570940985580, + 17722952663129849864, + 17699963590826942541, + 18046999390144526289, + 16551168589949339678, + 2737951381457117146, + 9871561605322426061, + 1712952029158494218, + 13804341105581865878, + 2515774586519545691, + 3055892671736160950, + 6710724628610805622, + 1412104293071317854, + 16497161007904304508, + 18357189440126213338, + 13603237157206851420, + 6273243960590211712, + 7944608681565512193, + 17876106042764502736, + 14798674142602476849, + 6953045780226967275, + 11587775192299104486, + 8475385210346705002, + 13371140973494856586, + 6794713226347140006, + 8193928063387091428, + 17367102755385777801, + 3555824590449181010, + 61277058838705259, + 8870120740632589070, + 8569261657911583401, + 11270438868333482143, + 4425327807117422123, + 1334182553156125781, + 1179127194588679902, + 17425871951496541252, + 14640393689292596147, + 15575431367431941091, + 10050699331787877280, + 15865307243306507597, + 1857750171635292322, + 18130938770314679282, + 7531133664044238608, + 12311758791340864819, + 8789821416232282321, + 1336876332854812867, + 5342090613788770253, + 8718998700193672340, + 16191452274236255652, + 4998135261355692699, + 13740174594907734282, + 14072068633008609860, + 16827929680059772342, + 13076448752571439675, + 1851555901541092750, + 6792956371094981827, + 14621930724363847451, + 5381649885728072012 + ], + { + "siblings": [ + "3697368111336814852788390728288168651761843580686919904705753453701564828555", + "8157863183369354001941938069666887778758163293015882555227352389208965697111", + "1839590469573502320128302052842569992161612731512161799915968707286194703851", + "15047361250661113398165673216467740394985222842468628270022890891741699067659", + "21174222224001178388501637557557075080272806220542533088437328642957710517011", + "13432454802250197378229694329139358748625217453066438865814518810679620628410", + "17308243007607931392560875761257971165048022119941135309877616223503237510425", + "16132417511118675772563615171705548345419868528894219693586552628653715793807", + "1386086069140630774358596478116050527874745004095021749322936924108264414206", + "1887113020360105652662812427880509995597812140399207135792857998036172353772", + "3286885105992486015096575778995364139525969434353456377206180492469920581835", + "4431994467078885193534287713040019539623543927214747668467426506317824549569" + ] + } + ], + [ + [ + 3683188128712646696, + 12467685144645901173, + 3829247226739253309, + 11589596607452418968, + 12105001842505782682, + 9731988610523704105, + 5527684778445703634, + 18161861000759996444, + 3556301222686362873, + 14701887422977382633, + 7877082953418399853, + 8304704073725917169, + 9236320453600710822, + 15168437757002237253, + 5248140237912148892, + 17167660376072466439, + 9875997975569301478, + 1999852464111255151, + 15868400892755244257, + 1440201915165974408 + ], + { + "siblings": [ + "6006792668377631579079480884740813784551388018205455833443115470906591536259", + "21056537149526526853087959820673223945389851826564881863246899994023312212220", + "15589564816634872854639756442693541136733153867564201707661369253110481577131", + "19105668431886128482629007158206621112422205061909915258665916535314190796080", + "8443215089728716708871084254062468674644827526379143323754998070607134753149", + "1516180912539113420217317531029129393047750480345640338926174643173857446872", + "15394358855171916606818974612831102038420851935760713629460276327597084752187", + "17739394223634583180839353078337463981343720689948270103099898079500917532350", + "14401428311962827617122497726728990686497385601203540994310204184722476410946", + "16319416607368778824146076811428585486999464678118616846097702868580577765723", + "6417694127983343415708748850913706642961493910752999424644393788499915769981", + "13377651578165513377462559574843959840121154298888589073842056219127158702907" + ] + } + ], + [ + [ + 13266758843258597621, + 11524647466422745539, + 6881340121169116593, + 8361097529067124805, + 17479554477924179340, + 11070327993863328904, + 9085848150639917536, + 921587189891868145, + 5400594063063277408, + 475583497948677235, + 16008705305925417402, + 9883449643817523252, + 2732154728014245124, + 10430686024590219255, + 10945407543702064531, + 3239449221117925091 + ], + { + "siblings": [ + "10508877493953398501486261658717128535317979548464755021716086407735252366883", + "14628749786603096424085889464486827231421399453569449407870586792199040142611", + "11207154699944222060193713560946496074773430700259799973107333036735353714717", + "11634803605374805690460571165452974362094861316564485413160465776930463497382", + "11290373769816903797364896564815190288511924406171093486486540882482124910003", + "5092803856474319924088713966269373583178616244888741249805013702201418534769", + "15057620251103845515503055690385226849177583130461484946078690627836345782579", + "11004420214184090588935333835186990187665516193765086184121312359133702454815", + "20305214852888792349816420605314919197087114385857086863150101788064056996267", + "9120420177945562262809230157305952963714133849611147655590585851660810636683", + "2044839066128482766125182295461919563725900701414871958767730750516362397451", + "19478007696468472378947095585832669160587463101328563412919982979727141863767" + ] + } + ] + ] + }, + "steps": [ + { + "evals": [ + [ + 14215483258861457442, + 5358912655976086322 + ], + [ + 3837215943743474350, + 5032579098721904478 + ], + [ + 12061625551178813635, + 12637524556866737255 + ], + [ + 16348790181836052495, + 11098927449634498205 + ], + [ + 9093367652456602441, + 809844341636108722 + ], + [ + 1053309584707248559, + 5662365189213118823 + ], + [ + 16647350156062223806, + 6936100629840990525 + ], + [ + 15478410207280199802, + 7564245659159206614 + ], + [ + 4118327871118298820, + 10999108633881635179 + ], + [ + 4197760280264106354, + 2632556760845131863 + ], + [ + 8545605110922954107, + 7651959429814110647 + ], + [ + 18391656052001680148, + 15825726311216338585 + ], + [ + 8370632460675782059, + 6316475397634499756 + ], + [ + 7540086414202595476, + 3953432518698668496 + ], + [ + 5419921352090263484, + 9416038568362569180 + ], + [ + 6653094586225653952, + 5982228434403769413 + ] + ], + "merkle_proof": { + "siblings": [ + "18443438744134526597529804478579138694838270940402593266579320488085829074592", + "11914111249423060069391263747022207701854899243759262535925522908563821071004", + "5724794398949496866109446239618311587622344428279223745579943183160811213354", + "10866805764302750656284383293974010863753862953000623619715940295202838851645", + "19752785240924197641511030337158966849880061370261642981349645477205969067490", + "19017160272964244606571256421197399569122029065061779313078625445868508660836", + "15367795410620928620656064141176785056908859475931333971843347997353820934007", + "7321070812872538139583286468340546406302931780446571823855108346772507123318" + ] + } + }, + { + "evals": [ + [ + 10527386003116779936, + 12717581320824128559 + ], + [ + 15265325084834169045, + 4953987769933598223 + ], + [ + 3658434804870366650, + 17103819900358128221 + ], + [ + 14569392492214655110, + 10561209245844374528 + ], + [ + 3288625335150295057, + 12693107428571225939 + ], + [ + 3543029827315268915, + 8352551800803475387 + ], + [ + 17797743807185141632, + 10208900942252309779 + ], + [ + 3462737020138368028, + 17210343836005822201 + ], + [ + 13371016901149546225, + 11182314746965963645 + ], + [ + 1222100973805861319, + 10211404401888183733 + ], + [ + 17660786208732000594, + 14623350766271575011 + ], + [ + 13028355032435200831, + 1037154490891665830 + ], + [ + 10854229741331275230, + 3514197728880625967 + ], + [ + 5947054438879512012, + 15356955295129210140 + ], + [ + 5077155324122659025, + 3066726772964842582 + ], + [ + 5144805648943486859, + 1872183940816355051 + ] + ], + "merkle_proof": { + "siblings": [ + "3172145761683187120348398457339206378840292277400553830431466063149428577731", + "9109703345088123836776487462146672880648486412140850410640369749113021733824", + "16839087879754769622404743522996461826534858399052598393758221189892642049336", + "3954838897038586814831478539703227450385433962414363736232707147744602217656" + ] + } + } + ] + }, + { + "initial_trees_proof": { + "evals_proofs": [ + [ + [ + 7819379790020725665, + 3510273627053733792, + 11581814790399205892, + 13457193048638549969, + 17986817476203421767, + 16903814432394752903, + 9120120578274686917, + 550305248354548137, + 13927823271558860492, + 16841125444831971339, + 14407867203965392102, + 2868099461092328379, + 14094308034290686956, + 2995501421440701462, + 4220505583514462023, + 302640952060430009, + 8878930700255816448, + 6581958186650358897, + 17514113012028182149, + 6882649419603005802, + 6136511481882826985, + 14173256629166565332, + 3869756299928736594, + 15821113796793621768, + 3742129780345672507, + 5941742706868928656, + 8423041992756067827, + 12106818739930719281, + 7036881725933942253, + 8932804853047656084, + 12632449409271442274, + 7781387596776026401, + 9554588174066806184, + 15622262158017513003, + 4854922243732819560, + 4539758906018103501, + 15043182375173271532, + 4915128873032838348, + 2686230503024004545, + 4942951248135726585, + 16293171755705946012, + 4912639036143173710, + 18307701418819049567, + 10414839917716975334, + 2083297689906109704, + 17117757351730537840, + 8828740878167407258, + 5363612099651432270, + 11696831317374297843, + 13627726303188584738, + 102759112646700418, + 4640493486336490913, + 10916892402296304560, + 6284474050719040903, + 4733866644115030148, + 15303370241981434381, + 12769809532623983670, + 11336313951699981595, + 6664953620032559871, + 17946470144548694145, + 5091754285277492017, + 7160100553900448510, + 974558201255996686, + 10633520682880470743, + 10705816930559907144, + 14725276838079715681, + 8018082004295331941, + 7771231743739769001, + 11007292466661414319, + 5923043755861504448, + 7165660422034199552, + 4996265802852486088, + 71956656167228769, + 6311497073568747589, + 3225605035852466304, + 16765040250486258553, + 6440148434970951755, + 320451737371879047, + 15207690889493978631, + 8924695887522829412, + 17707816461840502257, + 8820651884524890188, + 7162136956642022609, + 15785499568065842508, + 16064344393453310219, + 17111857134265292658 + ], + { + "siblings": [ + "14748479910453430045387568627709892918411256133538344538206371086382753722234", + "16084893921391681212700147257277275715736107797432345395242969696790161300", + "2186504744820401411406741333906558464568148347440905205713531014398274969377", + "105015026881787007902275421521654909763236874111198603456690620492089333701", + "1906412225032242345150843024730681102684999777879950568926166417824606909580", + "2650655428322089318506862301996253915917222921465093868860942117148221316601", + "3184483473522377680809170762934680149311000868041185876526213155738870322703", + "13341720855984358293423176341040742398315867580954748796577855491688653627538", + "19715788623775122633513855479297855640647346924003613414831357485243268125580", + "982790778597281784749557679722386089344426277972199432828031886365993347931", + "16103615601571773931816250555731656661308573231473550412980188580900668823423", + "5525458202937578395537109903285775408233276667662702384469394653661732201874" + ] + } + ], + [ + [ + 8877693153964155439, + 5779211976667155919, + 3805467481417831518, + 8916873215927436174, + 15843485111857876310, + 14233793600396117760, + 11756622665341867631, + 13782483612442555839, + 1530026035439519321, + 18328290596149475856, + 16076920975329892418, + 11792443788872562748, + 7275690829242294020, + 6254003887987900868, + 885377773931021547, + 17540336493155805513, + 17266671871134191287, + 1776716958539453069, + 6017278878973121734, + 10680950142785430909, + 740334348439464330, + 4580361223313685536, + 13960452615683337787, + 15150863451723852518, + 8267002692607723114, + 13856839803995298004, + 14021762004031685843, + 776297762722401100, + 14768641274149550170, + 7735248379011217695, + 4566569634643903323, + 17551745252938801300, + 3365370377074827831, + 13513139865355518411, + 12186881054603822600, + 13865915017118282530, + 15438787479117545334, + 3681906869917862912, + 14274078286370024965, + 545701556392699061, + 14183726367190622215, + 12855146445480314492, + 17551826215896335860, + 14328264418825393504, + 2342522701250036017, + 12189404811887353054, + 9093153968192168664, + 3032719140033587581, + 12289000233291439166, + 15257977590502068896, + 18127409016221664441, + 15777723579609451508, + 11071868465222276070, + 5275497913742906135, + 7495118234154854044, + 231331884522121262, + 8749392726137209658, + 9676101394591308492, + 2167468793191268518, + 6848240627216001758, + 7790473536868891006, + 7240222495263554144, + 11655344280449330411, + 5536002082154309557, + 1891322647702238121, + 14815644054367557385, + 15996423363119878834, + 6851296536591959673, + 17987311544473724071, + 15571053980491509705, + 482880471906352023, + 15420879491487007804, + 10507166421436046739, + 506464979800371656, + 7628579518725723947, + 1302844739682718610, + 8308059560779824785, + 2577285043500100420, + 7468899646513497072, + 1191790231686058679, + 18287959161785822762, + 13386844542311328858, + 12740081141265914776, + 18248035168629450024, + 4788591245607988950, + 17528206233310152793, + 14821838204107458870, + 7927671933039955220, + 1835675295772774033, + 1054425320261009693, + 890199174827246499, + 6673915020185214568, + 10475551322931134103, + 9176234443459088403, + 4265190653047308295, + 1983434755261980108, + 7820707035292902337, + 12992389349514171369, + 15189541035847622492, + 626763563825724745, + 5025337005095860639, + 9630725268368972295, + 2042947657902279903, + 4962553650793479081, + 6981984554715588680, + 12039993907711460486, + 10947711405691668210, + 8249854906041406872, + 5433418918466537314, + 18149343559063966805, + 14705734955673277807, + 5251172506879465996, + 15632441764650576576, + 10152985435938271939, + 18258457778548921717, + 10156530132624864999, + 1692519483836936403, + 1084791648871893978, + 14544269741684826490, + 8877693443663899476, + 9955730160095197741, + 17196425676066031818, + 11925330169236196449, + 15007998349054006470, + 9815321197149260055, + 13645204073807090103, + 17644947711263325260, + 1862047992755245968, + 9940642204855229875, + 17698915059084233076, + 13568830076291014745, + 17411158080192993500, + 14459118190094731721, + 2110664830720676318, + 7341129789045647075, + 6156666907825432711 + ], + { + "siblings": [ + "14813384394967372618866670978274782712735762577406574239116940358810578123240", + "11783427411274161596096290878068055476719838600854293852953162035911770626884", + "21419680618125403138241715512746101033879394016163971462747793309883727126843", + "7646850801232532875890806313793748386819045624154494269189219853427854808135", + "10836306818647207791260587366556044151855739049963560169194127819632094801292", + "9970330832406588482328780800256977381921159525534454183321319031300486779193", + "3889711308889451376891033288056672545694062621674043385066800749413330352502", + "18394692792780995773220059140811156354599262702935092921787447803243282691951", + "15183414363471681063443515185201964505827455099313973941089277230728570852373", + "328235343678942200431782967058349868771187766641781390192698458402708689147", + "20830615534654347106397732707564850434918942549520052791853468656057842110616", + "5925823132800086935619545549091316066939413373138591169426279734882159738518" + ] + } + ], + [ + [ + 6364010207994830123, + 7733390010466394936, + 10206689167024714984, + 17249900354749753088, + 1078120830409531785, + 4446386044417983009, + 15378680087903752712, + 12127804850171447310, + 16906635124935854505, + 7964382873892809474, + 10787250409647451557, + 14742410782969027602, + 6013151123142208919, + 12548746471466782219, + 16135985855776493197, + 16953444516579037487, + 16272669649721828989, + 9692213562057315791, + 12276784209318796353, + 8565874435947572959 + ], + { + "siblings": [ + "20961646077520912320400505266833208245954014442130451941948856378058051930880", + "16555264032128372771151278906201479584660475759787903983723546350608852784816", + "16288723345794609766313271100538591300381029764575623450450568647531957246592", + "2312976131694820435684031208118690429046419524109946025377248625025732642760", + "260636699315253088228105456801522790621868229290872819085998616818450619160", + "2469196678287304910105114723286234822576178273393345105589132110768903751919", + "9720180735653465320628240508382781103372080762950826614021748451106689335093", + "11368255768507180922409830461068996139512016150522410079953212082492219360988", + "20580830497523382919474649150813177316254824280175804247865374802831196215217", + "15441988614216264149546178054122058518584258668082139253401353626118816124891", + "5148870173096225590331546995372920639133652704762393302871187520045416893856", + "11492663482727723741068327332541580974937133796080767749237709690691695219322" + ] + } + ], + [ + [ + 9337406977378208628, + 13468321116766717146, + 14329411915606805552, + 5230503707347378340, + 6607156499483548002, + 4299882918704022391, + 14913073256778942436, + 14048573337169112144, + 14855266495695079253, + 14814261760855878954, + 16835135773792831450, + 6022158287311582271, + 15773248253378560498, + 7285233086296961290, + 16237375836074749843, + 14547776819769957365 + ], + { + "siblings": [ + "6667731273309295609667983258268533743433412841265842627415993069070774639427", + "15688079595516385106451395616397938997444874131710756614945177326879466325350", + "14309677586589929459530441506854540223819467703861549276500754653196926609227", + "3932373237421095488026549069678782494818687744028628931251562220966429606703", + "15122783709468530975030842040004153658017197324519966723906488224576366168233", + "2391981571963233058259279236550907675965326295608486336671223357630140243174", + "12110181665313232864781593720159228054705353653274761131676510558183788442566", + "20855483484609098939682220300538807185970107558204048499202715097971492692119", + "9921310433010680121109224735849126437463606495210960917626437657088497676423", + "8911837384731028133994016147731452418463887575275090562836328663508036337264", + "6497611870095904568125031537604184377110064087640138907849565564330825195723", + "6299650910743319602522179966700838070597065995155552516664060793479126759246" + ] + } + ] + ] + }, + "steps": [ + { + "evals": [ + [ + 11521841597890343709, + 7273153286107868695 + ], + [ + 873857409507915124, + 9175122950390827081 + ], + [ + 15136582428864437645, + 3704303527553859873 + ], + [ + 15551002219996841047, + 17349412241707681147 + ], + [ + 17869563692688486263, + 11644158116517163030 + ], + [ + 13234263372011001013, + 5926362947281050226 + ], + [ + 10225612621271828017, + 16186104143863967256 + ], + [ + 10258017772551364064, + 10082419344161210858 + ], + [ + 3843061433692230546, + 11272392095522463856 + ], + [ + 12617271593735208536, + 2153772111316400021 + ], + [ + 6959127720002387901, + 10451180772104843752 + ], + [ + 5012753180778976030, + 12944928469129171294 + ], + [ + 12951191709219239412, + 5358441396480735225 + ], + [ + 10118199723157440665, + 11167545334146720798 + ], + [ + 14267888543436897441, + 12399401412398398305 + ], + [ + 15861891182713746238, + 17797663092745217454 + ] + ], + "merkle_proof": { + "siblings": [ + "20816433201564695567661211191731291295651649827263251796128899965248762698167", + "16171976616119514189940850166277727355288035227319888154946612126296593392786", + "17360735637657856476023460289060236054808765649048226021286992438030827616839", + "7894850685098180369910752793140633932106729459505266878449873194139397239553", + "17200212607407022104407558077489988646534552438116871045200764929519206036986", + "7221599085882873998413405507960175175636518328530938614165155734383252851033", + "14028667057580712668023415688268656973354322726397467100796503008031600200825", + "1192885130943166989047183974747380893546051990115016985649530530404160835466" + ] + } + }, + { + "evals": [ + [ + 13793436559142648216, + 10930593803972088266 + ], + [ + 6068266514243161225, + 7765023863627289778 + ], + [ + 623557648584222765, + 16859319373459439107 + ], + [ + 16598086318262965581, + 8285256524945269026 + ], + [ + 1085237997560689337, + 183844415953475209 + ], + [ + 17817390803378374611, + 13308793728856929899 + ], + [ + 11340047499627115716, + 10811392574386560278 + ], + [ + 5849899646246145505, + 7314884926805029383 + ], + [ + 12841636361761007950, + 11095354828629344362 + ], + [ + 3346516839651071642, + 14204177026478649383 + ], + [ + 3370983679635896976, + 13549857963743954745 + ], + [ + 17627147398090418725, + 17618130214773720886 + ], + [ + 1957593617855816903, + 12691129403729489996 + ], + [ + 3591954887711036853, + 8232000676492385131 + ], + [ + 14612556681938607325, + 13235357250234723468 + ], + [ + 11647618952454443462, + 16379301797505256039 + ] + ], + "merkle_proof": { + "siblings": [ + "21459381451768569140353226402821709091888542575992751287335015537957710831777", + "8213653217508938258132913559451371585622480337244708217100377169573111379134", + "17720185824124973591267046446802543151748174196300070490614319471669424873617", + "4192187611365301383554644055403147599385443048897976890645855675846118522689" + ] + } + } + ] + }, + { + "initial_trees_proof": { + "evals_proofs": [ + [ + [ + 3946838386721479149, + 3799297743205104018, + 15160320429052567139, + 16664442550846064271, + 71255678605288689, + 7393283376802914508, + 16969609099694843812, + 4460615679397126333, + 114532312968786294, + 16874983167004200643, + 8587513161715974250, + 1371758233310441193, + 7552527701042894280, + 13482557251382373459, + 8547965091521360445, + 15509021491170906245, + 5854580780549721790, + 3663246621882458992, + 2062411062459379576, + 15063640596798172106, + 1111252993880303110, + 14883395379054484060, + 3204048728087630676, + 5333131001036210159, + 8550701892513415265, + 3241519574118281829, + 17470991323291818259, + 839357298497675119, + 11071352396724586385, + 7214195471941976375, + 351184364448014368, + 10436219488556864510, + 5368447313746300192, + 4483757031203961448, + 5517414170621299392, + 10067440812218488579, + 9016817610436410247, + 10925652016719611975, + 10557928124014821492, + 12588146877950430141, + 7268310883696526983, + 12621030401624202859, + 5363764061361207207, + 5404769619411181720, + 14424949661360216585, + 17532130119830148092, + 4220925704745464086, + 771859246446787063, + 12665566975623459221, + 3231460207272639840, + 16447533392317124013, + 5291394340280717269, + 5347986548028345480, + 12212661632656379374, + 990220974482030983, + 1362050340726241011, + 14259034646106434309, + 4915883359682651071, + 12962737630184771506, + 11456780314011072476, + 3709863607850906781, + 17911265346549267097, + 1529185795143493240, + 17215796082393228841, + 13413029757219885682, + 6680452905038514293, + 11977840571552656285, + 4236405128680933801, + 12310299699456779741, + 14331417980511807150, + 6984182633641613782, + 5053643007196841696, + 8731641758941690732, + 17035510991850266078, + 4208941855165875982, + 14839237658005237978, + 92484383144978609, + 13317141938338682298, + 11168453628182598471, + 10284546018815616610, + 11960269739083752536, + 9912729080375419947, + 1767383046783590798, + 516759605635393202, + 13211431793473562005, + 3313553762938834716 + ], + { + "siblings": [ + "13212243470451534873581306886538895022216731643970843014219986660001865796305", + "19518877525413595965886583584703639348107282337866028593052963859379967040291", + "4933881744991253750043143242122657861792178404595631358480930361703606707456", + "21391604187932469078717105395289921522542250433288350514795240141260893942147", + "15930320422642727463407355194544681949799976170932780871722184292875926840431", + "20610565189420113740509640107651887675278926025813848196185694534213367001430", + "12386502223168185175485727991325963738901735132848746435243242646638570391409", + "17387265146200598870189618027036513706057038552155881636496803231601185567258", + "10126239723382218475673254499113755468936264812595536568049862273899807635261", + "9674602399886361889691221704432103142352823285676156530729139469678986002346", + "16532474506923019047050211674323405413375559993820101088166674494818124502994", + "9750275698837768701223574958478189688502157177825821793084930487709394590450" + ] + } + ], + [ + [ + 2982539958147946018, + 14804590400711440367, + 753438129420590138, + 14505772542103749315, + 3898888867208508444, + 7566443821801793246, + 1695529701990302607, + 5590609649522088328, + 2686776614896200524, + 16084467367896251993, + 6801787866675177028, + 4516107456887674851, + 4387906350862016374, + 10419046805850244344, + 1163350919238105440, + 5604385282676474726, + 8449636801086180623, + 3145498891348098736, + 18154237969728975780, + 18021984527427975237, + 4506201634567414282, + 13712949252936284266, + 10849670991124244521, + 1232095823047259140, + 4835664140483964545, + 1062520172559643370, + 10225524558426724774, + 291175085572368098, + 12750264457711622463, + 1558601113624650037, + 16744574757666371057, + 14765825453325275968, + 12582670518985903860, + 11152571905421250100, + 2857192476874801009, + 4552168412655065253, + 10725994510815834232, + 8801497915000925021, + 359639706411299391, + 7456760893628019506, + 14776231278400632528, + 8562974029616188698, + 1418924408819408598, + 12644615181628649749, + 15684404614268284859, + 8504666504576614030, + 10791556007094896932, + 16837444457268369388, + 5752936335832803697, + 16946504715220989299, + 14908822083348539523, + 3604978216779071851, + 7993271740389009209, + 5783941379953077221, + 12069612504288364197, + 11201936709103380070, + 11865957806904289949, + 3233908623761279598, + 4246737933168213572, + 2287406520239509444, + 5821616384723892279, + 3247955829438379659, + 15383239197414421829, + 12356829438620195239, + 18218833353526107276, + 18375334319249087291, + 5528289956342384445, + 7732410875081224070, + 13109677400319081544, + 7229263389610737014, + 10902102646510068133, + 8151720060595547141, + 8360757742894725541, + 8409657652128645502, + 12548946880313571400, + 1153480260548377368, + 15919762348401307401, + 10878913793492906307, + 5088564985542023517, + 16679643856905698516, + 8712869463422729308, + 1035717812911594146, + 6454242370128722640, + 6730380619771931601, + 12334339248957023001, + 8223840145266129141, + 9487632885940332574, + 6421623990830813106, + 1275930071108940491, + 18312998309657122244, + 3274177528734998419, + 3509927209047876612, + 15124934333242260415, + 100912060147704188, + 18221491584630417415, + 17474287738133136946, + 13005842656305567808, + 11581023720930920808, + 16195352667074504150, + 15180319515469142922, + 15829449714233392463, + 6019893687585671130, + 16778675191210915681, + 633894111300553220, + 15449966999012902381, + 2835374685391220929, + 211383322542395018, + 12388727350754519413, + 510121084348219709, + 14431717447119940349, + 11970197244825050858, + 1928333382884629834, + 17440523436477824102, + 16842362094573185486, + 16676994612898402081, + 24966983628921446, + 17854775817077272175, + 3578652208257991441, + 3546731746447351503, + 10535200785437850893, + 5302155265538733413, + 7404507753690966864, + 4549729266644237090, + 6556743202418327451, + 2753400102007918352, + 12689156827563391311, + 11864969633213260404, + 9460708171114359671, + 5242144966359416871, + 2274918791949240128, + 7113534190712046945, + 2811025917379231227, + 7889558632179033063, + 11852776540345348330, + 11556727718415882283, + 17104400287769873022 + ], + { + "siblings": [ + "14463079065845774145774076230757972001306943636938840838009552729555810015775", + "20360106165957613487002524968405748274987196576445256746007419678350795880518", + "16355327189987113356754504270917736562471693958240327255331492552756599752722", + "8120408729923175273476950411229465220664580694648249410169839434299891619350", + "19940600132005858636506001752604910688376335170459894803669505812601928361970", + "4971681283385249807939969183856880575646921773518593432971457833766046681764", + "15030127676843731808439684404580861152035869626665728816448126180049913502721", + "4688186203716257827489942364843277059985166964901830348853675189119116230938", + "17330071628783129607387241587092160128383008347775044426861703025755144019570", + "14075191658854880545655462247325946324126551798369987091639647641643590357917", + "21124406909474951868612105277974978839219787634177303935948072047066472979389", + "7890754781305975405506729716910266690303142864758806773102488213972679649967" + ] + } + ], + [ + [ + 6961138565114289927, + 3702911017459279496, + 7743103389017804423, + 9150428632376806374, + 15123868067266885682, + 13339082472674549471, + 7484979967313455439, + 2761073550470310601, + 17985093873823862947, + 14127449348465450518, + 8140147624784881705, + 14284740144308579872, + 15160140632716078981, + 16587142573423732958, + 2658482067980782228, + 14269467478323503127, + 10876375299385093777, + 2634766818193982834, + 2761571850630114857, + 7181732723510051522 + ], + { + "siblings": [ + "1148611927797806235590412123709994550003788109134205630791935567544211573547", + "6718158313627963173881161628471464828340921612927802670969788575610355616525", + "3231037827901092255148920884064757267735008626048468144489786875189918636817", + "1992878405351390022206433098446055491394222460633505069830442514564907137261", + "7427859276269725583737128940284086905709933144845260876978857985474968252107", + "6807511285621306423903462528258656733336250851949144229741243723320896537667", + "4259901779711635627022112569147749559751402797696666974539685787287423241547", + "2772974350933598896749931507184305517733686652933639171706071304279005347272", + "8636128308745888132674701962869891585692854179410455676371850080887153646881", + "17864780282603121380140861304762052395077518688472575340956780812707553647515", + "4134472001241443864442271459569052534696832223595770915463317547753691158697", + "4645686635204857528115206928510436815037424022880425442735626162999325504392" + ] + } + ], + [ + [ + 4131954610009007728, + 931230508903743233, + 18162518601657069599, + 5015404091788017404, + 1075256002942408681, + 11524952406064990885, + 13859111921473232799, + 14771752135798570211, + 1775731066819327698, + 17454473462630700385, + 6282804206510998963, + 16879526963874815899, + 17860486337559747648, + 13901898455935681808, + 1154980917668413044, + 3040891111139671186 + ], + { + "siblings": [ + "7333864945558156755264374031144208729503279956671943470222648822952273868531", + "19766639503280888712722385916860109121255866068465024092841988123671938371476", + "14626175879962437442419113926604425350323613746442877201892684507145673744739", + "10344889928984144061690019569439758577328155154824392009635516816922257312105", + "16084412604046094597915796245465995633423361629230655974615329699670322604717", + "13993436501189161764127755648062503882703403351729552251780816975986859011181", + "3438395465288971874148045419045427787471896857482474705591986789196499111339", + "2419711735669808849080076251157845941265676342077950139284495330244595964240", + "16874042623433397177284192814527129931938783728146686059372325066934244199232", + "14197983578098187553814833950987085817484657531113292527555402789221619496345", + "7330341141577657877310578912062195121546232553417455867054668762704805371185", + "2803220684528112741544145756228290958289304050638797951471895119674942774778" + ] + } + ] + ] + }, + "steps": [ + { + "evals": [ + [ + 3595397537619897239, + 14410123513579355926 + ], + [ + 9867529006774027949, + 3029221463731888574 + ], + [ + 9093940118153171002, + 179341291176743016 + ], + [ + 11266570297666759099, + 12921171833265571084 + ], + [ + 17226328649908478008, + 16458311651483388275 + ], + [ + 18043589873523698839, + 18005819691501555153 + ], + [ + 6464336400047869019, + 3527042021209911689 + ], + [ + 5685635797598546703, + 8706877506539977197 + ], + [ + 13681491677173654824, + 14562357522534285415 + ], + [ + 9486238843718984224, + 8836346456714900077 + ], + [ + 4898672744232332622, + 14433289845683017341 + ], + [ + 4860905902732584555, + 12568681482283617918 + ], + [ + 4471061122012774026, + 11229801795342366709 + ], + [ + 2595142450178195412, + 9571646061351320247 + ], + [ + 5055790863737389772, + 6944377834485636496 + ], + [ + 10740682629200034993, + 7079394179800690727 + ] + ], + "merkle_proof": { + "siblings": [ + "3456717653171598763732564340856305808383447887596243622288120462837988247803", + "7057195683522510695322963184503720301849287136714136673293663363000693525850", + "15126904833601835894349450168729412068210485257891408406879595534711534763718", + "7858748226017429353675865908178337183995540261659743481064583763615812633199", + "9641292561090935452820505429030585124512421268081304772246934170779497336393", + "17842340188454207776660111368771465929910927499584597472463969726700001679301", + "6522453386893027206422415716167494886469701093678863887168807481670183790172", + "16751488847529873027307447641623379755645480241490915597843148188729131975905" + ] + } + }, + { + "evals": [ + [ + 4206000308726954821, + 6376017533892171517 + ], + [ + 11460547027426822174, + 6620555984488918171 + ], + [ + 13847482872471455708, + 12066751287943287171 + ], + [ + 18008988548431352150, + 17026177177266411181 + ], + [ + 604849154167356105, + 445649998318085585 + ], + [ + 18030352000784309374, + 15749279735053808818 + ], + [ + 9020673228215840029, + 12742232386235947775 + ], + [ + 3193902646056000954, + 11028130283558637640 + ], + [ + 3686797826442843972, + 16480884137309929082 + ], + [ + 4041271593647418554, + 15059989961105671713 + ], + [ + 11220702330646834827, + 9645450737628941134 + ], + [ + 1712629184533024165, + 232591737664304617 + ], + [ + 706449874146328127, + 4308517315706601745 + ], + [ + 7089591906921321759, + 2898220359820598802 + ], + [ + 2347762764096187557, + 3304191800883293731 + ], + [ + 9220154808349026619, + 13908535263542010399 + ] + ], + "merkle_proof": { + "siblings": [ + "11242959587647501478867000687837142920203324738857698336162076994071505865979", + "3121426021164800257181225647140873237125990731257423395034867197720195135718", + "5912124677484527726546469426503473269759369306814186940475212247139502697976", + "15599755975003728846348431118185513013282470412881316928351477434774149652667" + ] + } + } + ] + }, + { + "initial_trees_proof": { + "evals_proofs": [ + [ + [ + 9603738561291980416, + 6666267402203368901, + 8146556473915436754, + 13901671805497024726, + 14206362841090758423, + 11545147762067745255, + 14784573886590880360, + 15106322660184130652, + 10476230992293445109, + 548704064028388417, + 6771189339922708851, + 16027873467683953825, + 10618493876588458877, + 13573358994134072441, + 1325813822406088614, + 748595159629946430, + 2400486454369985953, + 6514064934179056440, + 9977530625639086473, + 12512566679523662175, + 7923117740336520844, + 6334778087563994212, + 13530512926026813556, + 3873238062783245809, + 16241935129772113942, + 8310273890794453423, + 2372856178968027241, + 17786700946862506955, + 7160225787686651251, + 15425200227855803263, + 12471627742706019424, + 13219212259704555077, + 7289347853234562604, + 14726419344028433747, + 15559866949007020247, + 14046861475503855591, + 6550160426049212893, + 7931711306222337487, + 4123691522357169207, + 8464566666652414985, + 1569163712927863198, + 10844974304308591398, + 11622509850392386240, + 3040987965469664915, + 1565994363074170231, + 16662436869687283263, + 12205802602147948112, + 10452300442467611270, + 940105134346103469, + 17080028264940495143, + 7718929072673981225, + 9643161552034463711, + 3247411886996840055, + 15955993454247905432, + 16181561145268581703, + 15329949010768341109, + 5233427047911403923, + 156895024202624389, + 10389091121110877553, + 656820418502480820, + 17256845818625231325, + 7410940066343737735, + 1730014416644685033, + 3756888979865856414, + 7265407649731358064, + 14831661681906317704, + 2895462991186689520, + 6063898480457175611, + 4564532126486123195, + 1835674695077473727, + 9104718773691111505, + 9767316178612854785, + 8112438996723976211, + 10206910105696260556, + 6803148822082718697, + 257096969573316456, + 14876339240489978998, + 4393569741359045095, + 828610048106699532, + 4438461562670117573, + 10967563602082270268, + 16906635900679763363, + 3265875243122097776, + 17195568964406628594, + 1227055026757040747, + 2487944469598206307 + ], + { + "siblings": [ + "9741691928132006480585521466725750355877656757547071269813460402894842142924", + "11138034126630432807420750128331803836513629831015858555047377929571179937848", + "16297488916718578351777619185857788410897081759021005224105585425660717090191", + "390549615752222598379893458764140360825071299721083595277581486413720835648", + "15670671328876055084045912605647375364377965292353474812918155378306691465207", + "1387166671054464360180715632819073196039087695720772339474431842165495561869", + "14498520840878971955359463694199246135345722074800736756049516573824386176348", + "20357234144721667501765432681750192227690356325223917984583013205081325924881", + "6183443491850564121729211737370328039288565098945303537683573239869999992270", + "12676565933892902529548469723637460406603396807699736705666541613904668462606", + "15548996507254871323936991587783305018325291618358822088650288020795704693664", + "3052389063881961436540442321815848339823607997419400655584187900535068367166" + ] + } + ], + [ + [ + 10664348813385068853, + 2689078963080759654, + 14279734076406991168, + 4753681112691739749, + 17628239030601259903, + 14208869125571714103, + 18277147090480825056, + 424175849379338964, + 12336758775455305584, + 15159021476987001244, + 16687638249068550610, + 17999310331260745111, + 5702544127805358634, + 3275486440794434501, + 16292696136043524048, + 9954447921310169677, + 18037684541864660447, + 10906976062906189991, + 6694811705245333587, + 5304316610744408117, + 15260604342778163911, + 9368739789013142497, + 16586372619111186720, + 12369704431891616279, + 2183505665133668023, + 17419863767806137808, + 9944705645002598578, + 4641644842810480704, + 911417828099908771, + 15192758659460820147, + 9373633329717695752, + 5211302897931232338, + 1528815824606587670, + 1572265227756324948, + 17576975158322701865, + 16374771513167132560, + 13226331388780099043, + 13066953066433462814, + 6872682806452515279, + 10110605968319784738, + 239697550846528856, + 2051832662190632456, + 3991155851728243705, + 2810196907422799732, + 3991624925763363204, + 8054786707297435394, + 14436382030322976285, + 10463807708667928759, + 2037464961039224957, + 13680989070136223464, + 15565625713633639213, + 9033830123364695549, + 6292506797731936863, + 6592300999497786634, + 15662694375110655310, + 17995288208295464336, + 8183588758949750191, + 10512843759743663824, + 11782062226196471290, + 544497182098605669, + 7393360499791564957, + 17685246119730469421, + 6791470565080226375, + 5822557432695062632, + 12740167873951836183, + 5574450140341124138, + 4267608321914510484, + 2319286314532312692, + 18036002974661230460, + 16317761295273056518, + 7920993428281095115, + 12120475742333064984, + 742506175823435748, + 7680440405124109169, + 58492864287249363, + 1035206682924663089, + 1078142576460504767, + 1770897673313483620, + 1224739183489608305, + 10329760725667496078, + 10252404443856483730, + 8267836816434407780, + 11428991002849897198, + 8011446451239958100, + 4770367943947151209, + 12395366661887614884, + 15040603196354448093, + 7230222979320556644, + 2777177634230091943, + 17523373378764971092, + 8140019753854846203, + 13678669258261860652, + 11721624194131514778, + 2350625696479047259, + 11681988725305320930, + 7405550740481698596, + 10375687197719311108, + 16328860642893565233, + 7140081915382990548, + 202165327711856091, + 743151701242941731, + 5361588222361703142, + 968441108025250475, + 14920284149047892420, + 1123619370282350440, + 1233382692462517993, + 8019774496679560164, + 4688946449312730056, + 1508812377689657156, + 10618526363094121280, + 2056663929769854135, + 295463198124676890, + 6084182109689639771, + 5407808223802617589, + 992959319773285535, + 8240727025901610717, + 15769684453375068888, + 3897414074079616235, + 5422460810336143599, + 4258333209997198257, + 5992748770176513972, + 7955953580460461267, + 5341189920201800102, + 3464881721449193169, + 16987271698714286998, + 13126434058982039627, + 17479132397249264677, + 7645418294368046713, + 9748833141142134977, + 16115420024695743757, + 5435910207636921717, + 3344008872821005640, + 5276719338931478083, + 9776397669094584264, + 7265154942341388672, + 9716295869749861499 + ], + { + "siblings": [ + "4768220275933788198176806935049971086616370914179788260725372960848961200888", + "17928412219452692747244629800934289961021972058311833822823005311313258850254", + "17414347714457348643168614993262331908325143294197257758856936362547380855465", + "18689003285021619336522912583108536458961942112735633844806309334597525080349", + "6543489575422306873801829642016722205404283547350167626309504068319285583410", + "15122824919929748692118254703374347082689250164718802984245239228890595740088", + "19784394341212738027245645906884173477704706873688822404470084697889978804203", + "3950927594111959649957272175531732202691493655529366540956762250593186588606", + "6684742064166833428641024907476839413887877242532550943933156983643613927714", + "6928949302824278723975609684472104906458235834345372018121033733849715368069", + "1134279433659963479054279935832187011417237195376709990164718285871726019313", + "19907647880229553180458063355832292580704725880150563757593183472987031111254" + ] + } + ], + [ + [ + 17480238046190154108, + 2985332718112462498, + 1280966101407322059, + 12220158169808754023, + 9329947415498090949, + 11383001428532418364, + 14804773012373730891, + 10573274854124755330, + 2159404377657565762, + 7530947175479996085, + 15149120988351499309, + 12087788722659919006, + 16204217075517562363, + 14517480288627688875, + 13504728062570647582, + 13551457940242158345, + 7442032112691047129, + 9040312215897520921, + 17676365951605168853, + 1911547370750418193 + ], + { + "siblings": [ + "16824661102537570758216474152074690961468606659449509614422602263840714473739", + "16525997880176567201103664103759471455510663508864601394400251415788481077167", + "9788044076138505000355816285499216413770839758094840474507811537546233961691", + "14039033877964974447918087584322696690194840017189755481568045871201822123246", + "18573071503832900090366703891938395977643577951603445317613243628463018497341", + "1492936447743068233577260558965306989206343414891478749810584817483856238346", + "11227225333776000463445516613347097571830373125037448453745040649202870966185", + "21401233525890598206495538857039593366921221864324351020802661926411582297130", + "3423728751360610428576525088874493499751909461103084226185893933504828937739", + "18944022978184873863465537239052938367188193592161451024043578117587679207343", + "15318466824707100993110386514039688936514764028772659696012539443954136688148", + "3558585872779213669309737306952931928333178068232712760299704133667436697122" + ] + } + ], + [ + [ + 7535903662332876597, + 2739907583393403065, + 18228395666019927181, + 10523070532456604405, + 6395067505290955398, + 6253522373289567591, + 18279467218468234253, + 13167838731849337490, + 1721340927713080219, + 4608567984458270610, + 4643885023923800630, + 2920732556419056389, + 13033628219105912030, + 10284899871677212863, + 10300961245503950917, + 1049124919464125357 + ], + { + "siblings": [ + "11042554095983222407394064277149764897835086169497195201040984737916855418044", + "18166304472371247546540488591221556549103396901521999107242075801314988090582", + "13653293012110728246984444840178288156682371710526221922537961792879401218382", + "9176872678194100301637816277548112227581704103729079030336317905119051533921", + "14316391066946771311534824077169965418781353367338162711679954035075869998192", + "1545525225198376263028161740163961803126436063044200759955080542698945175850", + "4361134361243513023969040712317601107195078429776801053926247687734821246010", + "11216190483250552146791295124682976778421705934266444186790534449165614046569", + "8415808677608799394045592633484383524470791210838604040088553866129882372765", + "2993598400861766005008941603338203784702390048008356964122032267092131987915", + "8856904178701854803101082739084867781834532557176261413922227160904759106983", + "8460210815005422617352224613560580100881430298936063407451580524578463703358" + ] + } + ] + ] + }, + "steps": [ + { + "evals": [ + [ + 6126171364303318240, + 17398101248950285364 + ], + [ + 7914394502175125526, + 6014864105883169672 + ], + [ + 16575548816725530942, + 10365799633467332831 + ], + [ + 17096574892200080325, + 15632468484611119352 + ], + [ + 9093780250753658259, + 10480732513252313240 + ], + [ + 4643047838095464797, + 4205123453218990370 + ], + [ + 14259131135115648661, + 10723184215926301835 + ], + [ + 4751946546174267869, + 13922406990695148061 + ], + [ + 12423475825285142620, + 12652892282626229922 + ], + [ + 13075964312392294859, + 11271639100763144896 + ], + [ + 9439510344222293205, + 13310747429658830854 + ], + [ + 9947555820345234070, + 4038516740186401727 + ], + [ + 18141372767284755618, + 1250904603118592702 + ], + [ + 12757716653780776871, + 808829842232055085 + ], + [ + 4914037965889560524, + 5740186852161278385 + ], + [ + 11077713685094377115, + 16775705572598700627 + ] + ], + "merkle_proof": { + "siblings": [ + "5707348174450348739915849294549035666113881340687097691096685002306621431001", + "15674335250167466645163472429623054840034124055666594489337610738853976404884", + "6860618047041444296145254555542084160564994344239221522213589058978703466723", + "19436789485921692064943590597072009978231088700697814351607727058268586693519", + "4706392414220047762483936630436040432614894052826977686246502887850680765202", + "4292261686244839798039913882703253846057962269377111644964654397306221193254", + "11684310152033714485194275803980489739969515137145711811046690824473940986337", + "1386464104167715077529067685264353096493867086595897860471132426790276041540" + ] + } + }, + { + "evals": [ + [ + 10779925319549593555, + 8234082216009584534 + ], + [ + 15513802804023235456, + 7138092120718058181 + ], + [ + 2788306814088889722, + 15494147206794817570 + ], + [ + 18417100252206656355, + 9965220910520430993 + ], + [ + 13604620369018456061, + 9523170539882567985 + ], + [ + 13570011000073301395, + 2883180657692489506 + ], + [ + 8420055083063078506, + 17028976843525722049 + ], + [ + 8288358513177447415, + 4477342559291782843 + ], + [ + 10711388689647569122, + 2957536361033106434 + ], + [ + 3849538386468443241, + 1287513457169673257 + ], + [ + 18093287948966263989, + 14715442292045558162 + ], + [ + 582148134597680464, + 2744798316548056935 + ], + [ + 5813665086134581761, + 8946573263313066389 + ], + [ + 4020684059129979654, + 10421799850904048764 + ], + [ + 8486808945264496060, + 13017277649972399290 + ], + [ + 4946171433405153396, + 9887143642438263265 + ] + ], + "merkle_proof": { + "siblings": [ + "7458900588331516875642527184505892458264713518151286711263321227521301444335", + "582244381519185436801080830382729357581121863448580085152864785577097824581", + "9052259441371016998472041330186733007801431716802020974058723817276563489362", + "4583047607711153260708918358925441022206255979939554413421385732789286686201" + ] + } + } + ] + }, + { + "initial_trees_proof": { + "evals_proofs": [ + [ + [ + 216507462898119114, + 9252371690483467163, + 2363937170641435911, + 17342422147592663688, + 5385750266181116841, + 6687263002152416876, + 5076309465741180713, + 12172084759242691666, + 7360291409185919703, + 3007420854821273969, + 17343293618412689023, + 12735177543820486028, + 4441861622463770454, + 5248123022473880063, + 2124773222527988054, + 4431509337096398622, + 7660389788002609763, + 16056284533616713399, + 15542878278252292758, + 14638367378930695066, + 4969889621350302385, + 2465646079177191198, + 15793698223520403094, + 4727064845301637714, + 13192623572570951392, + 14831184029022503622, + 11047791064170302432, + 412588217413466618, + 14102311111408212158, + 7967202849963727673, + 11812316120265630806, + 17576699763117628767, + 17177747756217825971, + 9313017454894524618, + 9643793491120788505, + 15298506139599827287, + 1748804498833619733, + 595149014850613650, + 13479297973591186804, + 4196298116203888009, + 2692091637289769729, + 2744583056703081669, + 3442545781531437897, + 17260394666356441215, + 7730413658974335435, + 17081893398578016924, + 9465428755442325782, + 8027672549762670602, + 3215246797243405864, + 3128265151694831357, + 15559570785048870636, + 2401215274313611691, + 8018694673595112747, + 17740488235851143640, + 15077259526871136086, + 12855893036018405484, + 10107982354446601559, + 6118098030679354664, + 2240726478291738695, + 10849499451901504962, + 6509885710922661662, + 7701451874588443841, + 11991296423508286121, + 17802143715819816591, + 7056399838871509954, + 12348013715256390640, + 11208914702956918523, + 11137240339666075452, + 17523039015014132274, + 15075531397516266393, + 9852014315061527778, + 6112607498269735721, + 6983024444847908663, + 23035685494597246, + 2510260742360018297, + 6108187884150221173, + 17274925721261371981, + 4901726733398099412, + 7419855126775573825, + 3384884289973340070, + 11376065293409090662, + 1386715088260008020, + 18283843230099021484, + 11085231768125797532, + 3764974802688844775, + 14859280222033801615 + ], + { + "siblings": [ + "4916869437877750939919641679251205030727738329292146241631137763748135251743", + "9740824598434883200405645932671303937652504192271464363606030333809515620477", + "1581128127033232873600889095965109102986041486289777737186451229002680902929", + "2269613142727954865728439602870735134158309286849662641559035048868916285113", + "9820919671660928284400157205003089585483752196451780391016789341397718215490", + "5671028739194800916170008162934288551291132461765046502801429423889405025016", + "5984992967784876798940296600195517721286812699049714932616369965862560507612", + "3293731629263714087069849005528582612466557240086081357907860896565499387985", + "21697606172538179954332117973598138196538571860293824116352908250150933628433", + "2712203416303225276848758088829942445338339434096594153816046689467984657420", + "18163204935251253130925718026888943403335053114195461826277612169654028494852", + "4851451240429149317524019037763423810535033317759345355295897553106794721882" + ] + } + ], + [ + [ + 15366733301209887886, + 10007197855420298097, + 5745504001627744133, + 2304772803469983855, + 7367421497558848852, + 8987453060411369405, + 1703687020664591895, + 17705863975090655121, + 114148516143812173, + 1025506238838870910, + 1894379207180642855, + 17928294733092978450, + 13705379829287316151, + 6988794126871002953, + 1978258292959385987, + 16548189287190767026, + 10525100440568179754, + 828989761196236869, + 9520132035295145942, + 1265447404764975030, + 6210406664929324646, + 1434224880663309019, + 15799251763848422318, + 9599110522764991421, + 11756514613059117455, + 9119480821341444679, + 6737075714842711678, + 15542252726859445271, + 9114639684221804470, + 11359806308304653035, + 13095794808351534504, + 9207686940788247216, + 12223101874475080187, + 9098975386777967504, + 14154734816919695966, + 9460522402717130386, + 15283844721365418711, + 14291579345801663138, + 16602718592183577564, + 8512561793405133711, + 9813998402609217898, + 973734900802801965, + 7296322752363737501, + 9830038683187533516, + 13580067705131052093, + 7036968779171279412, + 13437707714465851302, + 3704363349633432173, + 2622967672821539981, + 11332544052941210586, + 14908268456181381400, + 888624556237732539, + 14397724392375430500, + 7712549043795260789, + 6498687347541647868, + 1737243234686669461, + 10807842876044613798, + 11920219040380995967, + 12800693301230588304, + 2207967747991447016, + 18203491785773558449, + 2030720167360206345, + 7689318620760834736, + 9723358924695781701, + 5407932001312365942, + 12388577616131834349, + 6478915954458738868, + 17448517058306740655, + 2812623493263336385, + 6249378282660986674, + 6267401326029893981, + 6689992642544439461, + 4047487854348611384, + 1056512519073336231, + 2929471052442640433, + 10133940338317179711, + 11252645678695689671, + 11239928218155011254, + 16056307609639282402, + 2187976961845914835, + 9322979957966494508, + 16853872382930180178, + 14222232794328290618, + 6816997534955630399, + 6914664870551184533, + 11734018869097783534, + 11418916663208635588, + 17061353106843327865, + 1443451819426007875, + 8081377673876931625, + 16552523677101360045, + 1562189429109749853, + 15333988107177402691, + 6484148293376273940, + 11151056654154047844, + 3637184886897811170, + 15611036675970722115, + 10693714348549578337, + 11247622006950438368, + 15704862202059103034, + 12362018762973798486, + 5169537580036310908, + 8403358547875895765, + 6600498310272889117, + 4703535491547179771, + 9023614169244806819, + 7927101373191566318, + 18152712382472639529, + 8634182497719242553, + 13246642489195256643, + 2565270609429002815, + 15894558372983813854, + 12645866497699058886, + 7755038312042821306, + 6114662036019860410, + 59970946571947818, + 16455744776443919813, + 8760172686453264997, + 9994107005935325124, + 6556674996615256580, + 13054209721660852749, + 7817757768109492952, + 3578553275791787853, + 6297623134940409296, + 14344288434792289963, + 11444965450796796742, + 10717787527653150344, + 15481897248737486413, + 2381226815780053588, + 10899099678209322021, + 1889553955977243433, + 11281104969872652389, + 8864398339180057585, + 10950573636271348714, + 8910209249219536396, + 969935105131158006 + ], + { + "siblings": [ + "19245891036752169548984162884558407732027273482419158364403511650144751984553", + "15846490751924441712198772617265895896052777273012529082839992243934097027342", + "16372740620931043414452779980064659425983305263934892737918457047105090011871", + "5491971831913017521891799030968204758125121763950413836267166516074651028865", + "2185679840471917866177318100644097949325537897385542103401099810242903320394", + "4440728374106135521901192069657330764828357759817295962246864556985245184432", + "15950057163905504469586198660361502013463644482542143041511891141082718197126", + "18389689083537154303535852491838916726718889189046017473268279400845375763833", + "2340284758513820334330007424225996181861108917613038607474388502218221365188", + "18142931646994550140168480622804762198395347748584103263274954383868927872712", + "17858665496011792026267427759233309459816568901437881319329071022752171213833", + "7606272583016731538439988566093235115677706480993970384070464174447254167501" + ] + } + ], + [ + [ + 11811875564007726471, + 7210047911012583349, + 1873215387132757134, + 11331975687259109825, + 17522565094272485777, + 15592366086560028179, + 2658427735504201419, + 5197205923598292580, + 10425110251688307149, + 10815333979442912320, + 17170862078694354657, + 18007306540380406436, + 3877869487414683554, + 16479751618601327758, + 286676338245300615, + 889898675520555331, + 10788157359545517721, + 15093886375316184117, + 12391586198853437553, + 6313566799240204747 + ], + { + "siblings": [ + "8762898525837209990894689188977084550684539501910512330392555449925980739970", + "18786473874961240802115984333414722281764458647192993323363559489262697461964", + "19999430377772554165540427261390738370957192666976357507474937186750632438906", + "19523496406013786038508213135995685169798273439001554937335707667337032255580", + "21304011128747213970160925106018320855518039405858045261384374325777898282370", + "14151965892768846031309878918937564837355029164353785375519922360356915103071", + "7961881007611969912724836819280942680912328565839273684038957628082189910919", + "1267772954661913133050276397873895819646508087307286891217522023016928095358", + "18922461709411097786506167873876312194963434223064466848514277788481132966395", + "3092369293514710680936879820872216542962882169500722601138451697419642613417", + "3342409758973689821736824166876504099885238036833670551366926318766423363997", + "3695834156907596910657200631398678907951869053223671685327793445351339605618" + ] + } + ], + [ + [ + 9515139113064963743, + 4218630600825076161, + 14517366157399754424, + 18304795460106740767, + 11704649684658539894, + 10806274931502617816, + 15308315125641580888, + 18276669975204901788, + 12645546185803954146, + 2203592696839825353, + 1300226217004516797, + 1921762724049095621, + 13542945038691802670, + 15366266124856199430, + 12433789468117895425, + 4267524036727357298 + ], + { + "siblings": [ + "21734032048260529358183791790018118509844695723830597921787824795249279209881", + "19165001095189697183129475483524830131257899218427543722588615893575705063260", + "8393291990940858269618549173679964223275331657453890638350350896769416463436", + "6384337645118915983265127265299193516029281257935494772734724050701422359092", + "21014277484858989964365820071184419406418520430321633421188071448973942400431", + "8260636068328565653712062291194640302278019309940889906061461248676901819793", + "20332801996030904702246555450890553160313042531925244308874776137860779476464", + "21010103579002549117332108857200529385873378141897517767976909488671611432733", + "14808664172442219356124400818657185371632868239573069554329931724666498801552", + "2985054301010696786377044088175776942282034064465289835294983593696427244443", + "9593958876814000909468589350198610543223355497838593878346844855186315032618", + "17139669106667366494501405449754846786315900841213795917513250017998618893327" + ] + } + ] + ] + }, + "steps": [ + { + "evals": [ + [ + 9922888303008706834, + 5314803494590154007 + ], + [ + 6961811331923737032, + 3222193027292925193 + ], + [ + 8958788964551567160, + 51787856862480055 + ], + [ + 415483514935800869, + 10006435397443733225 + ], + [ + 17487118731494057658, + 7332476161342192883 + ], + [ + 15722213777235511252, + 2031239521900300898 + ], + [ + 14052245247598892087, + 6312532877958419609 + ], + [ + 8033897694183209339, + 9844097678784559999 + ], + [ + 16752672779196970051, + 660631491459685147 + ], + [ + 18157515393874562211, + 137833443224571498 + ], + [ + 4185984358212832969, + 11915432268327078538 + ], + [ + 9369180505645242125, + 16072657008126938108 + ], + [ + 8232587293102799472, + 552231633868604937 + ], + [ + 1721705677281597070, + 2117762100598900287 + ], + [ + 7478811748012843917, + 9137054575647746723 + ], + [ + 7242734313083202632, + 3849845441719190349 + ] + ], + "merkle_proof": { + "siblings": [ + "4355112208862925786670557781339058104951994747946455333695939371758021739723", + "15775581432055553438758310834366172463352777629595569432895616100357703834645", + "8748204012008630571330692081482095795640439095588859004425904451682400150550", + "9042041366323226871156186932447020616319942324143757141040338398888266060937", + "20752960411095801853494314237866322306782642625892842220584429465659719134946", + "14071188434587223993233931864703396235334554363465968435020969706277057955812", + "495313052960787520649481622762095566577616076051891819880771297920553920447", + "13531013533852933369842284620016165270465629708252041850544651139218758149920" + ] + } + }, + { + "evals": [ + [ + 6755465979034081119, + 17708586374728288625 + ], + [ + 13484839453280369163, + 5309886631861883254 + ], + [ + 15387183477865612495, + 15355987813029531129 + ], + [ + 10215967307260258473, + 1481872307022360189 + ], + [ + 14161763485807615499, + 7534535342144175160 + ], + [ + 16716017001577411628, + 12633475897893576091 + ], + [ + 15643881145100519968, + 11098818709622207190 + ], + [ + 5747789404774359483, + 8679054319030768235 + ], + [ + 16212210345437812247, + 2469980812087923618 + ], + [ + 4404729487864489845, + 3453096102984658064 + ], + [ + 2390745140692732265, + 1097198509380213890 + ], + [ + 18205941598873149930, + 11676128400085355105 + ], + [ + 13648177395162409694, + 14739697185352021413 + ], + [ + 16384823642176062380, + 11204261266299517893 + ], + [ + 1122341791815178858, + 5913852054976666318 + ], + [ + 15029107289693023605, + 16197153912772264932 + ] + ], + "merkle_proof": { + "siblings": [ + "8932386990099188613277474842693487340603359118944071834924879569105848065296", + "17102684851848317085819551937549318940570169816591989914648826741347743226922", + "19854506278411501128143743286406623836246277438147438035496043995020042559198", + "17345893519685647809522263582670930064868353535147447430168470803817175320757" + ] + } + } + ] + }, + { + "initial_trees_proof": { + "evals_proofs": [ + [ + [ + 3154493389600457092, + 8389518938246459916, + 5512580924560614369, + 16959236197195217007, + 16394755297574001024, + 2210266603141854264, + 92820745807349309, + 13566284008815525836, + 4455384469007357813, + 8341825085871763230, + 14853876889903186449, + 15944302212584790623, + 5234960542695805028, + 4797234697838917580, + 5888514460659802323, + 4014958677877752665, + 2659163414397620943, + 4534480876658022838, + 9310317131363049288, + 1618717488012162984, + 11422055091396377333, + 17166783911781001639, + 11814085165521649851, + 9418749338238677293, + 274752894690100740, + 8730003230270619971, + 15350902748994508168, + 7897799575389953078, + 4000524875252683453, + 7097823537695383442, + 1409858641482797432, + 14253099590042583778, + 10946619727924479938, + 12100970423309153040, + 1724741947208319053, + 3744353951422123096, + 12477873217556324830, + 9235352087412280290, + 11812913901420254467, + 1757853739149225861, + 7871431094604607665, + 16969092111146538751, + 10269359601563881739, + 17677393772359249070, + 14318907798843351628, + 10348137171036584803, + 16880072617304240722, + 9370128316567428790, + 10182903761598474596, + 10625743768996623796, + 4195105493000142507, + 1166544569235323571, + 14407988576678739022, + 1800355741597789307, + 5344106995750741910, + 12145239310275611978, + 10517869934538188258, + 10251928111519192482, + 12679308796896291162, + 15180593282705053329, + 11438917654434414087, + 5876146889926492456, + 6711403607845470679, + 6041133766829075396, + 16705503277483378073, + 18126401487813022732, + 16091056793373221345, + 6005196537395693865, + 8084362196426961860, + 13126231807236704231, + 7558384318720340526, + 2515995665955084897, + 13147959079194070245, + 4318258555802156086, + 3006294356207444673, + 7492103862973622386, + 3128189536769919093, + 9037092803195145045, + 8657770905973533136, + 3659097314956113111, + 8003626382794551785, + 6193303236568295710, + 14639638664797773385, + 9725604733326018881, + 18381480019822084483, + 5861291104559972921 + ], + { + "siblings": [ + "376811925525442691924743555338371374707117483553260250294505620760796966349", + "11236314543504535858066000841170799167929469796328271439934961447670514088712", + "4730655141740692017451854089401392336185984140393846203373608124395068106732", + "6510751396516406293319022985970333728704045193939758948333417339442532063150", + "10759413366260055454826043830586321349644094001484512894820253778662042879235", + "3414949751131825948249380531619332860937611298017446054621890653720157078719", + "11555105265147000736305191362622605507546202089615191628589723266553891343670", + "588786981588052363605747912216223208223419931836030038654444753993693496097", + "7073854451060850809683024708352948445540742856251034658779192850230353067900", + "21286317354463853264070352557962854090389149874263939171592806152585395731991", + "18026550184688394092931560844793005105443061141834785957534747761682293124727", + "8808092619865876568943873757207919964965518114424462894154004283305626150899" + ] + } + ], + [ + [ + 616530733711159309, + 6735709181563335297, + 8288351204513808532, + 3609899494440811009, + 9841768684288683107, + 5725707360640421791, + 15108877075856079690, + 4233926825454217622, + 5452013802526636009, + 15438502984077990245, + 12310695959743274231, + 6693461944871005573, + 2697654382370307915, + 6837922042604705908, + 17601022716527114699, + 5178525014364455037, + 12259268245346972876, + 3583304370090192403, + 3720452195741925759, + 6476103914420875841, + 11323929200825900539, + 14327805239292134686, + 11434350496257656736, + 1148943699871635369, + 8480125357329384071, + 928933415121411869, + 14361979774764273272, + 15105747392009988894, + 7858283872178485389, + 3477710369263762576, + 3533782537544761872, + 5590872156830500595, + 15868505296932573787, + 9226533899453184829, + 9269887306250411284, + 10033440152671540311, + 17536654895248268356, + 9670120746538119623, + 8836783703009363822, + 1518400251817550054, + 738541982527902723, + 8768765931844276397, + 390188375989464600, + 13912154120526320100, + 7622381434229864695, + 4852785577957562529, + 4135346168069125096, + 7273253822456254593, + 2742003904726431276, + 14583792312403615476, + 6597707241362466047, + 12530106209115344921, + 7949790581709505640, + 11911902175095954460, + 2368596667832501215, + 9716815631599127769, + 12533041081268817307, + 17749140067153732195, + 13238838696847717760, + 7578199759537054585, + 8959063332401894401, + 11167956092950050219, + 12728919319159445560, + 12511215721303932649, + 15546082623256796355, + 620413744446956306, + 13729662914775835029, + 16424186200722855539, + 10563885441792804993, + 14787512668025958047, + 13635524062835273323, + 16707774211738301668, + 4550828629288845064, + 10449189700186723107, + 3957374483313679642, + 16865525961175536568, + 12560147831712247057, + 10872810666309645545, + 4681502796826834146, + 7815688357955267370, + 13338062719428778924, + 1068446067963231105, + 1445828108940992823, + 15508840297144730176, + 16937094293937937922, + 3477350926246215384, + 16198074878856485478, + 7702096003385622021, + 6440776594497175879, + 5091750643563086383, + 10748894661335964159, + 11553865171462598860, + 9933607304443999836, + 3474589506388925381, + 15870897091197972391, + 16056147605477147819, + 2353149559273239642, + 71208173375400524, + 7806232599961388170, + 11293599863612989435, + 16842292312865600405, + 5412060519906326290, + 18017765984785997705, + 14238511490877669280, + 8959084891828700550, + 7355995509878911622, + 7577937588286940239, + 10488716450687766374, + 14801247461036585118, + 4022085083472181101, + 3626856138914771749, + 8365641343229013159, + 23863118935139127, + 14984664447058176756, + 9816345120889646339, + 11693241943723332560, + 4154803721562772388, + 13510770029519305267, + 3788398548633046346, + 3612063023598827735, + 6964538412467394403, + 15581644085306953797, + 16388966601354490290, + 12171556637919386842, + 1511874734891978106, + 5611608611496665077, + 14842040371393134692, + 9415105251703234988, + 7567981452598377962, + 5163233073089232422, + 13022714701910884052, + 5553469038844889010, + 10070168997488041510, + 1596572608913126971, + 14476730480571491908, + 10707799185210739343 + ], + { + "siblings": [ + "19552639826857610799078390378113064862550371814497843088682456175614946131101", + "20446890780264995365726989130335141915487906045581297264642207276593439483113", + "9888160210005904624482728961170921459715897974472266425181727316761203027745", + "9712344140518550981135908975229715205383343286810029419072294131534121539205", + "19268314576662369015482189574660767487691038710178435384369116491126514231122", + "2770318569718801745641079262487038876298484838050361766518997073850972078686", + "19563230166758952021869898683381712804453102809412768317875628246309380177291", + "7537948102669899129428235995301605071373511788853809741606619801549034008136", + "6963887994609777329892132228957275872987027839226684573354677956614637783711", + "12055745074297177732540593934633033747150929020917583137488088452015006345072", + "18816595484614675359932325128902571377221131356036848218551078168189123162138", + "1998102658276433662264892799502015512145849695386111169487227505235902733795" + ] + } + ], + [ + [ + 10912121663275268066, + 3462476653011687233, + 15237498355124449591, + 11382330728994078218, + 7250711019069983651, + 3561207007871791828, + 2786374720195799836, + 5178320941207448176, + 10632024714947835374, + 8799890839031812685, + 13065754906150652853, + 10426934531657241402, + 6270057277433155422, + 9352147947171971300, + 10546058983085726187, + 5942920567580128290, + 5171679889709776551, + 1430504856931209367, + 1523878314567358181, + 7545635133825723433 + ], + { + "siblings": [ + "20977508947141908391589169390663748453380877847101058990405061886835915157370", + "14048252411887851655055152766315704310186449674042485060259244084225797403710", + "150514283780564001431160719149746414810554910977337295258601693850125146426", + "1135485786385553595639292244399896651298551269737694716841539454757788233056", + "13923544196937697802245227276832467745583117504007422049436992649701141686711", + "544455752633865619829768494065509774271627034489342135109983061689157046978", + "13144368532984980021114903620634852886133126198472412028509218663422043415348", + "20579974376186198986473048941865020157739808823216826407422438222226645217223", + "4706379041241486626236172649025997349261290516292016127216321930843994531741", + "4969531110162792687652369901223943247801284756328517182836814138870235208157", + "6975775331299706229973027039866786809574977659508598167240396041574664084303", + "18166315801780454673186719774155956373640715737638090489111590402838431444289" + ] + } + ], + [ + [ + 12604928320795974330, + 6889805130229173587, + 9101071026778918300, + 11321053362656805007, + 12755503712799984274, + 11226099904096486529, + 17378079441412216984, + 1528517723057072791, + 8337214139265453424, + 2117541009676605821, + 7849581574727067661, + 5530181902422417900, + 11922651121487446470, + 557117056919225824, + 13232589449369652435, + 17346902728129173889 + ], + { + "siblings": [ + "5274754017631926952125757522170970716467651937862177847725667295680954761461", + "21174635925161492303609340581511550155006102831013574806965661440112121645104", + "12472098000561389470632605681128410431634534175778957099505173851765110749972", + "16305928824876826303768702494882335995745559592750356157766919663523804057486", + "5673735969956484494123616233337499871541561083396814090668684366939668960226", + "19673051925728811037867147899417173387000057764884375352618797487236340370602", + "596195870851857108265661516839135143723990677138429606383100142095322335724", + "19445106866948860037304598096024622421867244804629713590237607332295617185174", + "7686483737329936312563813856036263870706251317386770887447838870380489026790", + "9033803172310555988977426896651127085590548320731337684696730864279683123995", + "6281750628040293370664662711938862562280207318192463112779768107261726741334", + "20817810881385048455825782978372464151908370232529820769549915689281021813589" + ] + } + ] + ] + }, + "steps": [ + { + "evals": [ + [ + 16054202400617196356, + 6858863047307633903 + ], + [ + 6005829171715298160, + 13649877702820412891 + ], + [ + 14923400070405698066, + 1354154605508104124 + ], + [ + 4765970506470255840, + 15042530128999345395 + ], + [ + 7127544290989633542, + 13938138785673204175 + ], + [ + 9836944514395017609, + 16437332223437708830 + ], + [ + 8434626045738615181, + 7771318997951817603 + ], + [ + 1415061541205463251, + 14312183870768953250 + ], + [ + 14135362819607998248, + 17643603906734287772 + ], + [ + 2193748408090230801, + 13050793179556542900 + ], + [ + 10442195215350656268, + 16994969039724914110 + ], + [ + 12093654963825207847, + 17920063672300764201 + ], + [ + 18252284843566592699, + 13265068522423567384 + ], + [ + 8485833760811511707, + 337396187095798729 + ], + [ + 1385275149754439508, + 18217210333332258300 + ], + [ + 12461095227047740798, + 1174367077277545138 + ] + ], + "merkle_proof": { + "siblings": [ + "2964414401969686692093374331470803458929902807972693229413353663724505616777", + "4067391754759750657864929357499126883312541632191435808276350851757860644968", + "3766834771942296788072860701991431503789811615059642971437732966295986499724", + "986567429981802804501777696745530408894864326051688143550812677737602976370", + "10584243497625389700937855503718514042824341672108051468871208785172108120483", + "15860376932504935870542070805109563282906097670145043980042673569243685757351", + "21113811989086646924549433938810745056387415995799336612475781911734830176691", + "18796407632366312126747469892256705122902328415187205982153258190665502119492" + ] + } + }, + { + "evals": [ + [ + 17208224683023484756, + 11172097251337020481 + ], + [ + 8623964201787143377, + 15700095034299813840 + ], + [ + 18036535702382158412, + 17077580369936155213 + ], + [ + 14059608519842049524, + 4944685559468391485 + ], + [ + 13250911480336260134, + 3917745136289605790 + ], + [ + 12410222348675527837, + 6291536649277491199 + ], + [ + 9960002829446572589, + 2708474994122821272 + ], + [ + 13994917668316549743, + 16003709025871148903 + ], + [ + 15563347823926867091, + 10711817895810522556 + ], + [ + 14659499226094077768, + 11384665459383291026 + ], + [ + 978975705222388994, + 2576655558189894201 + ], + [ + 1924896489875244306, + 17058686963448511734 + ], + [ + 4493390650082739948, + 17085900083558914128 + ], + [ + 15105106437732151913, + 8431953705543686527 + ], + [ + 8296191896492001199, + 4439249678448563684 + ], + [ + 1801419973531771268, + 16962497760691536002 + ] + ], + "merkle_proof": { + "siblings": [ + "12209543840358613132696763617944715720338976528075030856794125991717382869040", + "10975234556773841821901698772077555956308199296711343207250536843635516155647", + "13577769404177141572214918377809286329260439018515864222168898591667436076349", + "16772845521094640194655599631071575564211278483810508469817620136835607719090" + ] + } + } + ] + }, + { + "initial_trees_proof": { + "evals_proofs": [ + [ + [ + 15620276366292636917, + 13724713325957538636, + 8897673336064170880, + 6016068710106541801, + 10577567952196800353, + 11867290176376364269, + 17409104894116844209, + 14987258559410777950, + 6055332520362890332, + 4606921731728379983, + 138805268564813825, + 6383867505386231007, + 11400637440967958723, + 8177479915302309780, + 1412456903940779998, + 4465938844091267194, + 4715246106350048707, + 8798095108451909390, + 305598748952339427, + 7673868679960284210, + 7340869386270717011, + 18134644161435497549, + 13435209816384840314, + 13089094060971186075, + 16165047821749165158, + 8754973675354491895, + 9820466894333588167, + 4339203811356573196, + 10082788037180800204, + 8645354878483870066, + 5604178013579423182, + 352632133184563130, + 7281244387952832727, + 7205875619977645975, + 15629880946684128239, + 1970651354030887184, + 6624636351514548038, + 1694430635337911720, + 1117424153272574221, + 15705641948898928679, + 12902031953657553532, + 13893247763069038868, + 270385055987059228, + 13262656273327711745, + 14666347353702622846, + 12546348422071525338, + 12907623541135531413, + 7654445882994922558, + 18353571144718389911, + 8001803732096634241, + 1118061425717166865, + 3687192474176969277, + 586184530431096888, + 1895111264201080493, + 5905982705770828768, + 18188068760092186335, + 3159765824585665820, + 12022964745953961240, + 11645294576346749643, + 17516191605480787960, + 14093188817935290766, + 10893713267734545913, + 12515406938126935471, + 8373590981975898040, + 6913561693176162739, + 8405779854460254960, + 10407411395519233494, + 14767398488212585991, + 11722487817162881679, + 9062317689765932522, + 12805970691612995087, + 16024121549120466989, + 3411760337429623124, + 12567094551845151623, + 8095036797303186525, + 17525233125044188422, + 11422798608037845602, + 5622314613408717002, + 15261058396866252487, + 2075666874746926712, + 16716329513292604134, + 15339513481096249351, + 6600910925874169377, + 5506063899785218335, + 15086625496010157602, + 11167475146417999576 + ], + { + "siblings": [ + "20687518706578378618320539348379820415227123904735843819591335178662794739732", + "15376073011685558645705294612273057913996646055787976038158125611639949104594", + "2014266376625371830371352354967032027231204260516422074808414335131648439938", + "19774503001480720339606878995475305047203235668392405531059836837631345921120", + "19131848329723242227421141563211404347911602602288005147871130440048180600203", + "13196362637949796537047889196741241752350765937635444148690852549356689256659", + "2968627413050930034114414553451387058446808570059835857519362545847004751640", + "19333232065798612854475877553621945584131563106094147637188566225992303439144", + "3506322298057098840489346120368957226546200541647739678753301100176805165022", + "20216824554500457124936301072704736642975704404660524041016414513737391907303", + "11962653073928804034288156006318453020283356565438547908128389439147802432972", + "20531359950793996073502242051998064322835724127990541525578136833693167734923" + ] + } + ], + [ + [ + 13398414302749306068, + 1848893319416446359, + 3633691179619532119, + 6683787722757172463, + 7056556175957984692, + 8310584629075301034, + 17917640904278792132, + 15651447766672112901, + 1573000369487274344, + 14982019333229694648, + 10375335699429940974, + 14799588312227882127, + 1815462176670280595, + 5224339914517959049, + 633503649156659090, + 13676651586667303066, + 17642108892989394446, + 13942880894704376051, + 10469777577786360239, + 9025992996749358601, + 16323526226090311084, + 17439289487970665528, + 6287026672954213698, + 7260883408402829359, + 14419785448061206268, + 15913234876958009608, + 5269147997047586982, + 5481495898167761136, + 8883589763486386859, + 12288696046013992975, + 6559948585147885183, + 12123285759202763706, + 13654139185541624739, + 18221363597029537737, + 15597720219694053348, + 7425967914826306144, + 9388132902813096394, + 11918453508413421174, + 3097205119434596039, + 10305830367334146439, + 549015535531931985, + 2365313050032889497, + 4217195260061523434, + 8749868145025117906, + 233520708364260281, + 12020307670566930579, + 15211620570596502744, + 11353941164512573306, + 722857175535013014, + 11845656976377826010, + 4738089796490856116, + 15140702893258899275, + 6314860292069216611, + 13779550928473077224, + 4902557329757753404, + 8738182554504718810, + 9819002318327833642, + 6197503916321725595, + 2594315248450621997, + 18391113481982001598, + 370435534804160840, + 10074695729832555880, + 3249609373856062184, + 13410577648273242568, + 12283946632260431768, + 5914376998276947649, + 4613907068067552856, + 8196764332897601922, + 9233417099033876323, + 8112704336008471155, + 5237457488285339886, + 14963166231050513717, + 12858267443859269123, + 14596374658700791701, + 6122823186423295391, + 16696128227575563691, + 17086771838184650555, + 3980173983420388416, + 6888483603544701459, + 9180961186055262592, + 7070875332549609120, + 2192807045331963601, + 12066339156653573499, + 897727927560143166, + 13724616769771652573, + 12043805185455682311, + 5797024450396326941, + 9396040754162512172, + 8250415585677980018, + 5477578867273870973, + 10231350351199544174, + 10827024915630957658, + 7232338305949363888, + 16524341181788517795, + 209271030821146293, + 957824624777844342, + 9105029581226398791, + 18004016907297592437, + 14201134125603635341, + 1813992976903789510, + 8150779950257806837, + 7238830150592273188, + 17802161483384165411, + 1108674836169632672, + 13427414016276405465, + 18217798056084433633, + 11285925279016291348, + 10595289803943289392, + 3533036718091458829, + 2416221781391942191, + 15427840941622430258, + 13733916750676649724, + 7190445621419562166, + 14178367571902603292, + 10238917896466200917, + 4536559449555514052, + 4819893648958527979, + 146440520166264918, + 15050410003235521236, + 13191752903040831510, + 8075123870285344981, + 7002768761542160997, + 17629622797954188455, + 7420314133207086363, + 12750688851706451138, + 2164542294696677055, + 555700598098212431, + 17130291449113944027, + 12902589375384894665, + 4411476050309632018, + 11981888630417198959, + 9154125466775756073, + 8683557890548727014, + 15586657882621175819, + 644341652126441181, + 9780350155552653226 + ], + { + "siblings": [ + "10972432660280000103950388969624411764578558127796480060512244643310117287915", + "12722658849646179543717780862551983234877977337930246509891741526500257692203", + "607531184481945177935036526540666039209181426042875957968461191833601380223", + "2884908281581991854198132140498584681443409120406300308706418402629672603405", + "498437952628161942894079800356853293167560112131327067854902895181953986849", + "16454174039712412457917236793138733312276560776355649317805909671336198261955", + "2589356181782102800179582440608971204923046146011215867461023278708276544620", + "20696621957208550191696639153905349706948732250568843159136969136384231727350", + "847730856260276751154551643742135808578068832200708435541478622625524480626", + "4896716569789183005081896437086479876274597505113000838857478458499678065468", + "3286885105992486015096575778995364139525969434353456377206180492469920581835", + "4431994467078885193534287713040019539623543927214747668467426506317824549569" + ] + } + ], + [ + [ + 17107072578889283018, + 10328746179092299522, + 11364858636226873098, + 14669416770812071546, + 9119805890252483523, + 1168434006802385959, + 12400291180205308112, + 154781946719075091, + 1444994246637355238, + 14459143016434193974, + 8949632294380950583, + 3357641247657787030, + 15060629439597134567, + 14697652893877353862, + 12633398418616003888, + 6567448137678581995, + 7665698712674502864, + 10621336589170045158, + 2348932117352711192, + 10210909876848136987 + ], + { + "siblings": [ + "19489114094797349315971774150047782156595170165911365104899687308075091194450", + "16207134530224145759938500283938611366097978591313271027856858053439352512810", + "3915477980461356080919378536184358146055005750695378836622692223966766937991", + "17827149237148183169345143806084432171842448193834787525279883629147521291225", + "14830313572488681106305342370965063056171222901888720015043856751035082235500", + "3134139816911367706779981113030093549770037744037756082141501147116707504408", + "12432783994473078062630968068582727497467536782661124149823423829956131659748", + "4838508734603294695928115211191273364324716578227325061049966481786642941481", + "4266423327309428428623383885305534413177475281402904381622298546652949799919", + "17046691453987890110065048109871227081995433469874900543206795627297813038140", + "6417694127983343415708748850913706642961493910752999424644393788499915769981", + "13377651578165513377462559574843959840121154298888589073842056219127158702907" + ] + } + ], + [ + [ + 1172427415639779707, + 12979167275121900453, + 15452376267212876658, + 5819721887558118098, + 11701143714376791458, + 9762591784505747345, + 7771534067460448175, + 6698371779544840683, + 5833835316572595930, + 13099545536699501144, + 16025225240942181509, + 9642110039896898768, + 8933447821262902811, + 1842608945763306140, + 7157994082269395553, + 6238388316542563021 + ], + { + "siblings": [ + "10748125858964458669059550007963561525465914318372895447644520791494820339838", + "8853165804835513071459544550399744509237488104787922031758760222472021461830", + "18394044566811663717044382894486026071023594791974937702917965640019315040430", + "1491454685372099214044004145852176674800636222802916956380422662795495770827", + "5496680146737029172091628700379937341740385298449197530708751868484560665099", + "7684537600116498525827017382510763547899799223988678634838608885125177409918", + "16206102291890265321597305271505338623201541670093756387543703904738283098036", + "12735303499418152988246857588176099700804442826521269866207623695984923862698", + "19055848380012281752026675150195139735761295217163728866219173089084935970744", + "13956313482049945589689276837024494592387298192877151093917482930699242191199", + "2044839066128482766125182295461919563725900701414871958767730750516362397451", + "19478007696468472378947095585832669160587463101328563412919982979727141863767" + ] + } + ] + ] + }, + "steps": [ + { + "evals": [ + [ + 14076446315951891481, + 18224353505780806474 + ], + [ + 1145510512708545185, + 10675763653980342026 + ], + [ + 17965146286767958286, + 14674776317048333151 + ], + [ + 18427373417421026171, + 14056180640573082906 + ], + [ + 5714334137202009346, + 13021179670759422963 + ], + [ + 15152227060659831594, + 10925169190567325192 + ], + [ + 1203240895080833814, + 2445384705706681212 + ], + [ + 4790354827399762660, + 17958316157525437617 + ], + [ + 9100041887513120724, + 3788146909058551276 + ], + [ + 13265929676973587633, + 15643369961692026550 + ], + [ + 17922423815435464591, + 5491435311229154691 + ], + [ + 2123753335435965155, + 12282947279612774994 + ], + [ + 6156964708732585183, + 14012262854931434027 + ], + [ + 4738980374113379579, + 7666839837790200020 + ], + [ + 15495995315322070235, + 1026203161620432624 + ], + [ + 16225163812113673823, + 4543780138213280099 + ] + ], + "merkle_proof": { + "siblings": [ + "461856220661110894526283935437651771778114647980081466210719566385751724859", + "8888408912485902416525322082169695591432368825534697829286344466626415909550", + "8459005908915652280780843486214207739537665596852533409949079879708092806724", + "2268757402047728573533448535567553284056657408043493828126221440604334881124", + "13791452945309336184973853434427085225266456349785629262610364204542702859248", + "16146151947519559583367374576242786212996985187456027123452521940434567417977", + "15367795410620928620656064141176785056908859475931333971843347997353820934007", + "7321070812872538139583286468340546406302931780446571823855108346772507123318" + ] + } + }, + { + "evals": [ + [ + 8396759358174348235, + 15913388692164818647 + ], + [ + 8781451081553931930, + 9986656324817478840 + ], + [ + 13820505118767658980, + 442006161771907487 + ], + [ + 1978815127078775295, + 2409246284775774039 + ], + [ + 1935906237457920091, + 14751466168193834565 + ], + [ + 7712872388070317838, + 10451965660782751754 + ], + [ + 6310679631711812135, + 2652800557878772642 + ], + [ + 1889237928876953354, + 15205293053479136950 + ], + [ + 16877176242093739813, + 17376067168712942878 + ], + [ + 13990604898166844404, + 6371527169957111613 + ], + [ + 6649094035333797377, + 2130242092588860248 + ], + [ + 9965145227601106512, + 10998936582956829760 + ], + [ + 17006230684823475681, + 12462708916081922950 + ], + [ + 3065033195098976513, + 5185790521265262226 + ], + [ + 16049977071953124844, + 6531161769929940076 + ], + [ + 15482977820435345333, + 12494924918936392859 + ] + ], + "merkle_proof": { + "siblings": [ + "11896767155738606162077642038907107747497146554989610500083503807378556166425", + "10320153554540694159743323141186624407603811514730210714641228753159057876537", + "16839087879754769622404743522996461826534858399052598393758221189892642049336", + "3954838897038586814831478539703227450385433962414363736232707147744602217656" + ] + } + } + ] + }, + { + "initial_trees_proof": { + "evals_proofs": [ + [ + [ + 5425484274179025611, + 17153259232334591299, + 16107361878553539825, + 2984329601328091713, + 5507279153710147421, + 17882914298356308785, + 3150017895657133261, + 8667466920368705703, + 3477807483295411825, + 10305270137996885232, + 1397956222096722705, + 15449235906140151933, + 9122022932286939592, + 7591115089361523912, + 16005119203214219591, + 12523186604532114909, + 12714080800935260791, + 2285125556011064100, + 1045938615630756896, + 13513777937190606985, + 11245029133947586275, + 18009865528051905722, + 7503508777933997553, + 8872770156455131055, + 11430154960122941687, + 14098629177387797060, + 6273681932651961160, + 2270083452691717447, + 11474619094714569323, + 5951439387083581536, + 4925091876117893791, + 11542677643874828809, + 1616702823980734730, + 15732495478596281664, + 6461648024101458378, + 519617051835241253, + 514916199897012206, + 9671027711948666305, + 3779597418010226730, + 18276983970490524988, + 5574724418351666897, + 453903699103347294, + 14638714212225561638, + 17128757849160300526, + 10358373154422982690, + 12740366227410727480, + 4869759535129056263, + 14996143214752609177, + 9146359735741912339, + 16520357445997211997, + 7250753258174625992, + 17108562906757864218, + 8535800379888169866, + 104603344027633335, + 8392162481218134581, + 1247844813701476053, + 5807884075662886579, + 14120943096399231016, + 7108596510539326805, + 4046594113359303761, + 15471600703575002798, + 7297148437552337845, + 11177750280639725955, + 16237299475271212553, + 5648459117518085467, + 7834262997272433343, + 10678657310595901752, + 10318420385727821, + 2902151690880173692, + 1028642781265458605, + 6199435113562163031, + 6482984326110759047, + 17250408279137347043, + 5487929623730363278, + 11655414519663177325, + 5692297785301909455, + 12879109936731578859, + 6844712982029825361, + 1306705058614906110, + 2242012375684295001, + 317346834721760792, + 14317322610520698363, + 4635040124044763825, + 3015028389654676841, + 13754184277330647702, + 16877724213197112856 + ], + { + "siblings": [ + "11128278052124274838761789997674438933971352813378995215569341671299190245851", + "13929960807946962301920015837311696909315531391306940294073575080366463046565", + "16311991496436954956630453903528219826852435837600659917930277608798350729530", + "13835543918770282491240298659166907743189627548031906243311441580977718249833", + "10203995368949634843622517714728509664649086644699634854858837736258917127958", + "10856468645877968856971308472214684643512334469587618192704224392293052419594", + "10089686383047836109743409189889004642217945159369207235811730372371288471285", + "19287004620954933645941801042925740944687013040779377318989941823499245665031", + "1256997564054126769274439580965007263066164809487370842638768998645176483578", + "16440256779914242357990231474392205322782483223180613179429621472542332077396", + "2092233531330642101866653194619210508066835110923247815523253471748295485187", + "380175320461370641357063966780764745976226517077479824583101052578520155415" + ] + } + ], + [ + [ + 7973737222620353200, + 10731765740117360979, + 10912810343724495275, + 13099254892097105863, + 16146281426372058177, + 18406530473210434991, + 7697499109400801791, + 4621289555168322776, + 10991483091250500928, + 9601995139524736819, + 4522145955342820678, + 5411600401536478738, + 6166885652353394306, + 13890840228522269732, + 309333730576228768, + 6885532761517191855, + 6666908776942838102, + 4293180841146380024, + 14789732227624589557, + 3502887978629545146, + 7511921551320806865, + 15376247819044224530, + 3710389471395546281, + 9476453470765414074, + 15270805966096535786, + 12758207538320820317, + 14126051399776061875, + 12997906080135520752, + 16677902863116440592, + 4393481597876050791, + 16852758690422560017, + 1583293043209539240, + 15655091911600331100, + 9351658643139894111, + 10681764447562106987, + 66042285655915468, + 17199451496575959978, + 3693379481170823185, + 11756187141540171014, + 6078470966070484338, + 9206902535564249593, + 8121102034090038746, + 10445628373381609126, + 16572818844465804277, + 3320250560788952272, + 13960837002928746281, + 6264740264643934566, + 6405991460092323615, + 9953519910776332550, + 17027427787104994796, + 17052698422835605399, + 12599238548832303180, + 4285634342949173917, + 14948138524290318966, + 13689856227150498535, + 12829970960650353179, + 4231010253431718631, + 6507739383688864470, + 16981173670361716129, + 14906709452817561437, + 17462964006579218845, + 9739856734137689034, + 13571652731198373987, + 5028685071490118742, + 10879134203019875378, + 11663345913044599169, + 2228021300872720408, + 15748072850062926369, + 5236232451104667840, + 17342915771009676036, + 18011005929761850877, + 16043772179695085820, + 310790728891916253, + 14396552896941961466, + 13637923725460801863, + 190490827191643844, + 14374122072247567895, + 10815253213349561198, + 3553951199513074348, + 388581000348411137, + 1178131355783585318, + 10007841406718986542, + 15256472369125596964, + 17542634611936981785, + 3493979356341457170, + 15549436495280515871, + 8961489315799613104, + 5083493741025634762, + 11016687607137503366, + 15562338791352256886, + 2757043578853724181, + 10082864240561882827, + 13553701947625045139, + 11531966893229628133, + 5992173605450525863, + 10878769806255402391, + 3749299866923412223, + 11256497731140389834, + 9966465583528620907, + 3204540369409767126, + 15340921792908400395, + 11948162660257075506, + 7440227227420185634, + 9732063965850867808, + 8185872884912138088, + 17980159272207416160, + 15136922958693227372, + 2222031416541155351, + 8710882774406717055, + 4587993016338473162, + 4960448221063925400, + 17171427772541526417, + 7400631682414087240, + 8662039760787539091, + 2531220589409145510, + 3778900459050700733, + 8151333139583394929, + 13892390745451377190, + 16284448222467945622, + 118708176656958120, + 12496460492107929315, + 8108296032785028944, + 2085053838751603221, + 7777648203027108140, + 16830623956361721131, + 3342261611958101686, + 1516844753020276765, + 7936131674930418055, + 9198467542660913028, + 14637759635662440905, + 920603255211627360, + 16490438285366257548, + 16938270776855009141, + 6903698032729889968, + 16871492286165653051, + 15819831855452133173 + ], + { + "siblings": [ + "18440830818431530007951673284180142011520881456380903168840447801675633881990", + "9370650689883434310013122399137121370363035236720296758587045347150638022155", + "21762361663484259835174330928430331255867865890279890246930431251970159560687", + "16091550482964097331010708932078962744064126805542591534303122274310453914330", + "3120625374409601666841994033829304355318259246131914148443894337886141746514", + "1461428869411723338782492321956003400367801832960827180152023618239253434369", + "9655530296250531030918247517680509271992766303838049922190770678096529111111", + "20459560584643731379943348780974948758011172718534357727815048201256081301536", + "11158307171224228719003350794374352591584146197448627801344711242702214550282", + "11252739153174254865014377734388194606860455423659368036008191853485618908519", + "5678403951486160155835192106862618413428901951787558149198280929819850970547", + "17928170776516354025394923402300442733002045685469719916720988207501729013852" + ] + } + ], + [ + [ + 18228798500122813274, + 11354070981247108931, + 7839354525499378707, + 8577237507853206571, + 15618353276604227735, + 16286741828346158558, + 2369700003684297471, + 11667750214218954388, + 17523082969081787392, + 16258533265461264823, + 404068734634163095, + 8225825198490870957, + 16784572534120068951, + 3687759118051990393, + 11836205312720245348, + 899655784485991082, + 17444066783417130379, + 7529813117526973926, + 1513665653537318591, + 6321074441536150836 + ], + { + "siblings": [ + "1364787036345954842879513167345682586620880333783617733185330224570486668376", + "7645990465026521837608935813072567177194539526034229999874542999734965364892", + "11568062421828781869950939812683661773581957167524110269924007254071415430399", + "4210158875600338858778102579369531847501957694592262326625667690245781928865", + "7449543035612889219451061489540516964428119209071635751947419797215380686842", + "13324412758651157991242323770595242866702900400853257414152681556665650399904", + "13825607416023782435183514595507180357788881429297986449812227897689233807461", + "9441655642971188997351897175241419286356048745519212897621970533598081555272", + "13689885690943310871948495627158597997035342770906324276611408071968035606802", + "4357566020164334884020931367918705588582557439400902586105719434337636909635", + "12414378414223316385398115757187244688676332904488287296242628523199576278705", + "15829279189926942492331359710259740871899684824446119455749978320246330388136" + ] + } + ], + [ + [ + 9937754880498587743, + 12557076485298961923, + 9861052579902885375, + 6830273172677671099, + 4339575960306809285, + 16924724431780605738, + 2345819853644680746, + 6623205589425580173, + 13588735073621409298, + 9917882887141344871, + 2803531987458140784, + 12212811285876646694, + 3107156381982169972, + 13698757887050878523, + 78920145385638679, + 18010785391165977792 + ], + { + "siblings": [ + "2564359529788554565064227060531102507191354812016845866257312248907032889635", + "10803064147305967856497640307106245076510181304809159098864046654506140013517", + "14831814948198702419741834434409238254897608459657614060007663926014351960760", + "9006240867916347343668901992399610649533652767176270025211457283146987200705", + "579894436220684670902411325913641269211209250805329001017454074222202374865", + "16559396356035970457352014559018704210144771099101633317304348676922682048488", + "9630993253992644558724820118271914774118321362366930694886675642185732652741", + "18539053836868320949715115764056608205547737075354663965478741934703256479769", + "15280254861763231746691616208359603278911652520708670401391892334158341871206", + "1790681167836778606064497810132285442081510452208732704459762206617352709571", + "16557732747831220364046920470820930942225808585123678871926537559701838708120", + "13560029670498280517591022599810080782963260530436663735204869544922429707185" + ] + } + ] + ] + }, + "steps": [ + { + "evals": [ + [ + 11462853967951002523, + 10389990320121618520 + ], + [ + 17900867435622581774, + 2144137952940452234 + ], + [ + 5878591688424708681, + 8394218812749423987 + ], + [ + 13464682719357726513, + 11652308721094571563 + ], + [ + 8651488042859396011, + 1776124207554915439 + ], + [ + 5643766534958904296, + 5334583299706667979 + ], + [ + 6578611769873167764, + 10806359182673416841 + ], + [ + 16693650273371373489, + 13757220482818195147 + ], + [ + 14152061729521009867, + 2548126586020561494 + ], + [ + 17053335087647444797, + 757467639265841974 + ], + [ + 15793791821536193785, + 9915743720514128540 + ], + [ + 10632597391819443719, + 4834435730326344302 + ], + [ + 8537074971552521366, + 14231847834007972200 + ], + [ + 3528930690213923667, + 8292986547501448091 + ], + [ + 13371968828563510020, + 10234111843433088365 + ], + [ + 10042996141634423035, + 17264754215331623144 + ] + ], + "merkle_proof": { + "siblings": [ + "5764123114924985012560788810445305613004630832661999019643647124123154133502", + "15045533367792791437193038093024345652716637213560463355800027527838349326891", + "10659889165584807891241168898382584151726941310597585084765484133263986546951", + "14057889373180695846881411962582253962453972813665728257528503938604140118013", + "7249961357731097639632197481865712199277944918799523391176458107646732735314", + "7036519078470366142909843212095450641204842977829431736682990321475434305553", + "1415172791413240681077913087235075746255321771166983339670080108771412925751", + "14007624440094195121247165706853957844373153338106633103853118106615019848743" + ] + } + }, + { + "evals": [ + [ + 12932534599032354885, + 8880761471484892982 + ], + [ + 6679864086432059202, + 17743384969767885701 + ], + [ + 18228478257700223064, + 16020224910633191438 + ], + [ + 15145753854183248558, + 170877061215845634 + ], + [ + 16322730564202689602, + 8752096523218811131 + ], + [ + 14609797031253256917, + 3613541758683074698 + ], + [ + 680434751556495087, + 8292911119811454554 + ], + [ + 17005896363397036201, + 16223026715487229229 + ], + [ + 1089962243056177276, + 16073168870050722400 + ], + [ + 12809678853551679916, + 15764750195660932312 + ], + [ + 2028755992584290597, + 6506108229033266795 + ], + [ + 16357304249618535618, + 1122823717017199042 + ], + [ + 3974053826709677637, + 946560029976492106 + ], + [ + 12070844875622596483, + 6462305171084600290 + ], + [ + 10070618144751446947, + 6723624325402524815 + ], + [ + 15669897168685420604, + 3139794431813513085 + ] + ], + "merkle_proof": { + "siblings": [ + "3911703103431162589233802413983811635017047713942207409082777391168140155888", + "14082865728956692244123195914784827991706249006436561417280852550155500664197", + "475741197625023805165999545500117355774520782014331653252984017060322612154", + "184289888923504999742621315664051145043133940116103002966333840498981047281" + ] + } + } + ] + }, + { + "initial_trees_proof": { + "evals_proofs": [ + [ + [ + 7790407648833972715, + 16825664654498397684, + 6580100578769379595, + 13123468641480782132, + 7038671862838577226, + 6173270632254914988, + 14954268387981929141, + 58474064664966652, + 8780825920837925424, + 17414288983075156179, + 6081648838355393267, + 734468845004924348, + 11827491935651633240, + 1825271074576312175, + 7674156041840714037, + 14419403556265712061, + 9570145313890391200, + 7605309683976829567, + 11302997651647801771, + 16102388611443638276, + 15862710973675258390, + 12142128417722574868, + 8671228070639307241, + 5580866093953823670, + 15459515888366567253, + 9228555526093303428, + 11184446077562321010, + 17410464721543939758, + 15232418444226151537, + 9053689011637769933, + 11046619013213181363, + 18269224358527883271, + 16029273821604762466, + 8198030734297267279, + 17547520452762324720, + 3765962573060337815, + 10298990547034391055, + 6456730453090616684, + 5517060065203074764, + 3499013989295147904, + 14484841473613447143, + 3762640483255055350, + 1548628196715317009, + 4787796569833846540, + 1937659320758875720, + 17806181459573537060, + 17557694936810884836, + 1684957728091580529, + 6081552042766247449, + 15133158939664138644, + 2992501674416318866, + 8629761013475775016, + 7563192725072308790, + 2728349492079449070, + 16881480815646781160, + 16244415781376774558, + 6322234465171918417, + 16373628516909584548, + 6688361063771129400, + 3688834614755091509, + 1273954948113364368, + 15149349035284589709, + 13255166367209404327, + 10156973393500604673, + 2702114574364846932, + 2963587978096389528, + 6564812402740403101, + 4786206603848200127, + 6821097479724911739, + 1853836079435452553, + 15111239986089740090, + 3950650767839432561, + 2087036374850617350, + 17109292049560646229, + 8691959218855123572, + 18225798463704130067, + 17546665375022108777, + 9786741538312642684, + 15451567540655169108, + 9492185098385786410, + 8817101228409570989, + 4607116666525182332, + 5362527193843695767, + 17592023043513072613, + 16646457331941508489, + 2274709021052303004 + ], + { + "siblings": [ + "2196879591941978504908957148167654113293693504789088669067072056591606692923", + "19904846802927826053737447790275442195412353417777846787093046624794911056469", + "8878707691087487206856038285302875066195399694562047625662251661292792918638", + "14727493284086576059868299452335289847966099904231728521979515977230595090280", + "1059182483948499499663735349533166900151857515029181468679468778504195874773", + "15841105986653986347607201022070020670732256916796832827972545295105581393003", + "21574801126786854548435249266676494212674288091477725477295827879618456244801", + "20682880351329093962329496106231957663341975872069863110142001875090736813134", + "9935989646824807683092955966398794763331250687903652887624976949787938824291", + "1229173534050630398382886045754227698300952477126982454722061939934840539160", + "12471876078952103109239957443901309464881885929496350261611923706923396375402", + "18336556461154158953330734156204028673801247292781606589601026775287021707273" + ] + } + ], + [ + [ + 5216366173073553060, + 714572985405771255, + 16509542670606459311, + 7653120519894424420, + 4058003633600891983, + 9180355665638459799, + 17651778352509203709, + 9742324581610434397, + 15289632799652738207, + 16419392463639115190, + 7573360890550163863, + 9949373419610049778, + 8011960656057973901, + 10898731899965239458, + 13207199570761719504, + 7032658719927890943, + 1047292703691378271, + 14522113260527812770, + 6777970661941440154, + 6061315311386846841, + 14722777144863057217, + 13803763228263415960, + 1865225211231893388, + 13129499408747805434, + 11872361649163100003, + 7893657490524278480, + 6023834736000975344, + 17067196895616965546, + 3168802558837325975, + 11998816351495082937, + 14432401084746628749, + 15951777645605325021, + 1200036122704598564, + 2522849203799206188, + 9151486549548203371, + 10770372617764817973, + 10919171182831580663, + 13399753397980294141, + 16499915656146034118, + 16369017669449935326, + 4381975458044075450, + 6219927843554034191, + 17751039473314513098, + 7562622185327044078, + 13649866121638215525, + 17826175342655446575, + 10574726534062344121, + 14769099186361241376, + 17726474266846525666, + 10766585720189794581, + 9105482626521263275, + 16911824486034212384, + 8742112856599687691, + 13035925174379722744, + 5401795460081444854, + 3957194712867130792, + 6098755907128273791, + 11568329610016549310, + 15645545011516371577, + 52768301106422519, + 4114860671152760700, + 12120127503420851742, + 3734048213032792745, + 18161327564893330861, + 1944021460617779114, + 13307387975066046769, + 13032709042766835815, + 3356310413658795757, + 4677236608482752677, + 16398120790993690617, + 17374524082649920556, + 11250989546837507405, + 14521662545683420420, + 11766333113588048066, + 12288222744908413091, + 2929135894410619127, + 18330924473956868069, + 3366820718778146994, + 10148071353189801992, + 10064399613076805515, + 3162379250014589313, + 12438352562799593735, + 483931625754761449, + 16793609748782084410, + 12556226130456266644, + 14441879515740020791, + 9121249068112929702, + 8641809940807442128, + 10550558045647396115, + 13997833036489379122, + 10144557979805442923, + 8138179883191929436, + 16890602565896223607, + 17283097175478847693, + 10399089610006149069, + 15466475463351146191, + 11246341164605082182, + 17030141243360157404, + 9567167334476129134, + 2877242404266139374, + 1172064115761612593, + 17508200704319455862, + 13680387670519755265, + 15939683589153030736, + 8209252691784758068, + 10626422660648076742, + 16623356362129864590, + 2578368713776093625, + 14597964147318799562, + 8580587255151912902, + 4147371899887395833, + 928679616622211746, + 13132771417929684346, + 14043991958619432720, + 6635288573053147153, + 11079602041621155901, + 15307266864403943175, + 7722766001824374604, + 14610128870829300948, + 15147269749634248389, + 6118847348783165464, + 5417522299386635851, + 8955848593096792763, + 12096635808526279008, + 13558072620876382909, + 4153090988351755267, + 5780285673861202802, + 353110202212270424, + 10744753526966822787, + 17161006776338315170, + 193527845171626532, + 10194707633983524974, + 8856481769773855597, + 8110914485787125195, + 3170010015795415803, + 8735218605066117958 + ], + { + "siblings": [ + "7247459218044544830252240151584185255924716453106197582851355707530126443198", + "19193164609166544468027015929952932234808336153203212934283030858053634621089", + "19381087224308033676429444734668956772521307298809550445147766412588810608446", + "11738764145630404687371419858839924161825438127029710914413200145514776452170", + "4397961271811472360969868963287639647974614938967136237621000915996252862046", + "1091962031046403936672033937596551575310884758843583863563943482942235505168", + "4684501635811071635659595984463497070776055258769191009418788490348331090103", + "610607527524865733695391210390139967421371357579162064606990195504980326875", + "21301239774089273489743525459131675956323544367917630388154143830848652743375", + "3602917937585921753906761384133411949762214553364345734038418258685963328866", + "19194369642096097116519839116066988079168707623238763405286593583997455845048", + "8385127020566588343035272683843043969904346010819239743097190743264563524917" + ] + } + ], + [ + [ + 3502926305917849399, + 16725679784407026570, + 7052693928063086309, + 9713763945959908712, + 1602534815754079854, + 8570387868038642820, + 9893844280475327520, + 2443126982515742528, + 18243209622471253838, + 9332196482634899419, + 832065390080767178, + 9935034485762173482, + 7711269788793130509, + 6715320959485930840, + 2727076814108997536, + 16387532023620026948, + 2362159383750062893, + 3900362148778608134, + 4741309280546877504, + 17861168943066028781 + ], + { + "siblings": [ + "7481907469971428903354715889734691714541427624745669901020127091800422312062", + "16617119050472373090053365032655274131174471237275106743412702869318409387824", + "15756680892307148004358350481322530081067804842965387216567197556445511461572", + "2514430525205963286131130727782369407742558612820947924021007598716944528851", + "18746776922614251157016609596433368050872493159921634888337198554597553332017", + "16441446664230805999872565346870499970187230983148091994197549495264957740455", + "19450692346572513079688027139903383957375286729548278602545048169247376829290", + "4475707804775447148346821496119155216479982419903237453959540240680727236523", + "4449921986570666863202253412018932619467535675704571162665423049700803909621", + "17663381085165316915465131653732421194621662821962927490541242530627863155203", + "16318154219648239121847186317014539950283339636165078568188833495058124593860", + "3798814720411754597177065328948895690125186800844657363837407494785883711259" + ] + } + ], + [ + [ + 3412193227495540975, + 9761410427103458377, + 16566006108057911946, + 16032350449759979997, + 855621454395293621, + 2984158327626374828, + 3033766006473644923, + 12373669868918840489, + 14858090070114908016, + 17141729198011182659, + 5764342720803530148, + 5587049639733817355, + 4407267167896632756, + 9283877369230543120, + 6027084494397632660, + 7161988271826631567 + ], + { + "siblings": [ + "4875958658629108118205315602146951033245427428158108193004156363772297703549", + "3905180320808671368243745432702347455328833206039695818277146920352686945006", + "8075613240249874634487868056750431784598432134764549493412977751530899354079", + "2360484531180159881404000748723893951184522158045132729624149234731664777645", + "9508153409924086360196201650936079737617966346742298429655214476660813379269", + "19771827743601543545415345495712296139387281809339599614394529732112172670254", + "19409358212984855021366548518660100297133416289160093068011294482844855089172", + "2625382191901691935478199934480629835377987262803924040964999833980245846905", + "8292912810331042750083852875095144262315065520529263708384577533113503831138", + "13980489775659273039600977357970410823461554783671518605648575359502409959133", + "9701193966719491890663990546467926432933348000294391882958064462518947744246", + "19524790869652984562395980257533701695017908079884155559094358581488948384180" + ] + } + ] + ] + }, + "steps": [ + { + "evals": [ + [ + 16479271301448203953, + 7303048014127662202 + ], + [ + 14791783319292309384, + 1126290559947107373 + ], + [ + 18315879728965775296, + 5033149431560989044 + ], + [ + 1141902886911345006, + 12434282737169886704 + ], + [ + 4391458316150577601, + 12350142737769257633 + ], + [ + 18175300563829894346, + 4223031183621112653 + ], + [ + 11740163312505826060, + 9869509575851890853 + ], + [ + 10073349516761318471, + 1127841595506703279 + ], + [ + 16363077424841851441, + 922899701507847195 + ], + [ + 1371607462229966896, + 2923664036380487358 + ], + [ + 12587568239365133787, + 16720870805661422976 + ], + [ + 7255296425525558502, + 10496733505091800213 + ], + [ + 6479346662441726366, + 4149065335879178734 + ], + [ + 6029277294469906855, + 6590669052618083117 + ], + [ + 17233163912723825561, + 8897669247454047000 + ], + [ + 14280743879986635518, + 17592971551717684887 + ] + ], + "merkle_proof": { + "siblings": [ + "17610740714202586428958736950506295588298773918484885568712545873179376605491", + "20070708375229221181470024829372778382453238277321305027082052746485541788022", + "18056276927919260574764045618781200140325344768568075978499512097184407532370", + "2614884790261769994850399205107038592187103628374533217079242620371304824930", + "14524430630179660496783479445196951954424266017470959764679750686433621554508", + "13043664562649752469259659250941203952531268379262748387723823063069038243598", + "8144115940804278669066927007234872984382746926046168658567787418000119218963", + "18475098617156176236145675448985833706987788030213443090611745375016487928547" + ] + } + }, + { + "evals": [ + [ + 11308124978150067664, + 15480384784882751824 + ], + [ + 14366403979664708118, + 14958984559308071178 + ], + [ + 174945715777168487, + 15391622401888010840 + ], + [ + 14927304510335501920, + 7227547867442374750 + ], + [ + 4987920733250793636, + 18405345558438949288 + ], + [ + 10448482615983316313, + 15814178510865888289 + ], + [ + 6579876576389678427, + 13144870247945638559 + ], + [ + 6371342431482910153, + 4528200360972353681 + ], + [ + 1956442308947217268, + 1968714578545809943 + ], + [ + 12826165226166545086, + 12006164424370873274 + ], + [ + 12342464825267549297, + 12399516405846633309 + ], + [ + 7775131958810835851, + 7526004685590263594 + ], + [ + 11634263558842785588, + 9410853997620129216 + ], + [ + 18160251193768486935, + 9296116181296489462 + ], + [ + 1337592057854581641, + 4687158105268352542 + ], + [ + 1697585650915598604, + 10304031235331748401 + ] + ], + "merkle_proof": { + "siblings": [ + "897878533712530248440106386765881485308462308082072376329892098435651131653", + "10659507083048123817316850199851157916451517910338985148406973149649505635970", + "6039517037677021689879864249381059105732218742531216407774657358174337135665", + "4765790185302443049742269279827183235276733623367862793222739954904205860811" + ] + } + } + ] + }, + { + "initial_trees_proof": { + "evals_proofs": [ + [ + [ + 13507544937565713399, + 2354441009780146271, + 6298966980463723531, + 16307723716794582503, + 6134185874836097617, + 11655683456174040307, + 11857645882561438149, + 14144481406430648600, + 17681289587306537322, + 4861265557200668889, + 2569682436769974131, + 3776188620327748115, + 12066440124188120636, + 2285584651426256148, + 10916473300870665997, + 13049265026480097205, + 18391797541483218966, + 778597931411412470, + 18369650835160787047, + 14735211950453252276, + 1145554878923965960, + 3162037109606110908, + 16881148447849323957, + 14845711323195942210, + 5426547793156750327, + 8439311880456487422, + 4768066997095514627, + 13895231067013851183, + 6379471239153325533, + 10835219111049861870, + 10810107306541227400, + 10452902671320563762, + 1000797569732576500, + 14111866974391427656, + 2617716610038398287, + 238015535645674765, + 7033258000072642084, + 1568252520594074228, + 4166809855197289788, + 11819199115386617634, + 3781626241935740146, + 15030114163307804906, + 11791214725796495339, + 11591277908878188064, + 17290108562788410196, + 10368752923071300475, + 3741667862168795767, + 14264278253694804366, + 15064932175533785651, + 13340966324913442059, + 3408137474765350933, + 11022113890555451616, + 12556573787793029566, + 2349290850709278921, + 17063936424128891563, + 4619779987842273164, + 12678070595922746310, + 3822396460925686517, + 12394223404161714387, + 12394877188325010104, + 15525455161307437730, + 1536409308207028669, + 10728343327076270450, + 8579121982506396467, + 15715208057189619613, + 14239862142652460104, + 9817216014836457529, + 11824753789837168097, + 1853425009686261142, + 4313669471017499653, + 16264297598681524763, + 2692018211004544522, + 2854024274869806371, + 16187060456829774750, + 11456293634529749865, + 14090618299029442633, + 14222132635727774080, + 10898065763719677767, + 17652923865714803893, + 12390953563128487827, + 13262949711808548305, + 17587700740582822797, + 1415429757630238962, + 9734910519752431926, + 4997334811810809944, + 13770918068280652000 + ], + { + "siblings": [ + "13321516396226418675201910421648651235150912916693686110424458530046306408211", + "1483583841327263331192499969999538949351570358876023818737745348239959267253", + "10255370534332028404284173689481131802649044038007601606291917345073254686186", + "18017883852537350730509397454759790084929621644300138440126157537594783160234", + "1313808386185028034388792500343020745451721003430653071973921137370716147787", + "12472377136042684371584596885843816847574834445112431927010354517538302094056", + "6896575647696553576643821763439536823454895116219558899115538496602211616067", + "12643264602308857628579061311508317712805495843679362188821953762957667158041", + "14829249968676257994364002876057572793077189415138531862575543301793111740615", + "16440256779914242357990231474392205322782483223180613179429621472542332077396", + "2092233531330642101866653194619210508066835110923247815523253471748295485187", + "380175320461370641357063966780764745976226517077479824583101052578520155415" + ] + } + ], + [ + [ + 3428951253599179909, + 3087962666200130445, + 3972194647069314831, + 14563293956503604534, + 6245005964461837377, + 16930253439240759565, + 9110912801593523662, + 4677465638373599923, + 15552116861466433311, + 1645224693741900595, + 5841639161299770639, + 3331816735514980559, + 5510253311851198205, + 14784952778206117708, + 5393100800768828200, + 5099048134151081183, + 1975106199378199209, + 15693650571846706828, + 6104631890902073538, + 15718382291607735999, + 4846753277911376252, + 16085056077699055758, + 12095712234418949714, + 10905859749294682855, + 9863426917972574674, + 8967789930434441658, + 3309516190102177128, + 11809146213043011791, + 2490960348228416335, + 12193500167710540387, + 15790377413470305329, + 9509546384862827467, + 2816748586954459813, + 17798669855807022343, + 7435187527056722469, + 13973716161680461847, + 15977422369719406288, + 5384944448484697740, + 10727764000484620039, + 6156540406850496115, + 8245211258115373701, + 538314841347442179, + 1097980358330159569, + 3068544141331054456, + 8533083821658301493, + 12429626593264052813, + 1470144371862405461, + 101663218110020859, + 11752903801720549840, + 10495845140167972986, + 17956259416242862684, + 13755762221224501981, + 16406427388755614711, + 244948330664676133, + 10482391356415165224, + 17903684212989045766, + 15794814446947058666, + 2022925984460297566, + 271688850873636884, + 13181100729170727037, + 16260130644653655331, + 10201393695981328125, + 8641782794363510296, + 8718233822913947492, + 1765327048042788946, + 1312109805256224393, + 14654278695230655704, + 12367374755445535543, + 1716608399473585050, + 6648321294705172179, + 5769682419447746782, + 10892445572775361817, + 6388394495705757436, + 17213493284315066027, + 16372292240906778299, + 9614969054282286666, + 12900581727360641939, + 17754956653891686189, + 11418209829103520722, + 10702863085798984065, + 14282437524597880723, + 8894875930599844807, + 15901692724832269780, + 12794632728496181088, + 16278499428729373363, + 1066759877390374591, + 11910610107036005391, + 15668251105651874718, + 3048068756824979241, + 6075515817996365318, + 3935909033744930362, + 15816686073989543347, + 17968059971746785537, + 5768576891193787486, + 8838381219067031717, + 13903810035508668983, + 215879290536400568, + 2143184308699424659, + 3710961366192597004, + 13424201974954838935, + 6285817433631093286, + 931333053283370601, + 4944935685615909999, + 6113635823837290848, + 8775587517543825574, + 5812395907973718670, + 9894881444681751182, + 14891645407185251254, + 5165729398490477954, + 7033576627295388427, + 347016307059049243, + 15220297256154757881, + 298771660019832767, + 12889439196218365872, + 11642255021231901954, + 16857441730577860114, + 4594143746655151668, + 246175506117314621, + 12453726919606934075, + 5416726714953575640, + 5135261381889941430, + 5759675281186555343, + 12564446414347277190, + 3670553830099592310, + 13651957595319859530, + 10179258146000178674, + 6356669828308049454, + 2990474540517959956, + 8415703867557575403, + 5450716165183008681, + 15195489102923156786, + 12480685094212048464, + 15706829785293126774, + 3661228186236807909, + 10993159884282506312, + 18319084053101335183 + ], + { + "siblings": [ + "21030624425514448415248042595421447194064435967837444893496345609174950987695", + "4210577599541221789066348322545319492362521950700013478627451292118806658748", + "17729195634901118059281908970861755240493931107872229559958043067217500062477", + "2742013535689780987591772554447584974146521358856111642697942898817668956275", + "21472060717101370777470683211230436650184965738308065936086150852431448844867", + "1631415394232614971764137458860454381341053145959203413814713553940434705224", + "11741446152977065875697127478818199377030665391636032351441671989627672618172", + "1632019481001388699270357666606425653118727731676609836530841416450437603070", + "17220730524041564067093461422403053626242915454455398846892105270396729493052", + "11252739153174254865014377734388194606860455423659368036008191853485618908519", + "5678403951486160155835192106862618413428901951787558149198280929819850970547", + "17928170776516354025394923402300442733002045685469719916720988207501729013852" + ] + } + ], + [ + [ + 13870336766366879950, + 3615933065283432512, + 10686364216827029254, + 8137304971935992057, + 15974323099521605144, + 1123075476676407048, + 2412619943114138418, + 13785881096537210633, + 17310163037702368490, + 8374321898026796801, + 3664489223289524774, + 1852730573715219451, + 5741476990903238961, + 8610515397969920400, + 11913864063253510075, + 16773677817234322967, + 2057674521867437908, + 3152441428613975381, + 10913987552428205281, + 12744093975445811705 + ], + { + "siblings": [ + "6979854571422304998063937275690279931649078303974869423645025422652603127780", + "513211955177514159763566126703101677387302549396512461097800664605839382540", + "10491093505708645646220345608733555657561220445628361602735628831951060739641", + "1472942753998081323182651328749310053523554695026038638009228206598403493982", + "6794428629763369697454282929562741757743820955637187094174795776661500690956", + "10365523632318589619144885060533315392887807716844709063990392621627152759837", + "15694132578019445828874728964564607581656856342724668015904367494522772189770", + "4809170987069705889238514531148829688075080887089406824418270006788621355450", + "1085781240815411416849077203641134175817048721203478315141532883301152385239", + "4357566020164334884020931367918705588582557439400902586105719434337636909635", + "12414378414223316385398115757187244688676332904488287296242628523199576278705", + "15829279189926942492331359710259740871899684824446119455749978320246330388136" + ] + } + ], + [ + [ + 16077120925344350191, + 11095505594309009290, + 17467600435115282254, + 910346762230053334, + 6732500966731921032, + 17820653619926277317, + 3596840152718059488, + 5426314620327356931, + 18127823733310763321, + 11765375575954919380, + 14888031451679944038, + 12866563418812680843, + 1557841147688035600, + 12356112417062682908, + 4253668775446697042, + 14632485842783187863 + ], + { + "siblings": [ + "16110308778651298731019065540220608652717811062894921419974161094279102512486", + "9961371907214171595274429067171617525468519061721182694670672200432338679086", + "20869585912900537299450477575960023558591278379084602500109767026299589721261", + "14741564206576586553594542601959388050015005553755645927952237767085807039320", + "17701264527268699968064744127257809594596352604086657182346115833847987261577", + "572593952487677445128030830867316354040570640360591706137167292664987739683", + "12572873502336384001878390346167954067779606900019007903255843370442046141072", + "12835761935147421429849150027745997886401517794849774229320703813405377848342", + "10077513604113263725075782840129989510479348898133630944880131755976853486655", + "1790681167836778606064497810132285442081510452208732704459762206617352709571", + "16557732747831220364046920470820930942225808585123678871926537559701838708120", + "13560029670498280517591022599810080782963260530436663735204869544922429707185" + ] + } + ] + ] + }, + "steps": [ + { + "evals": [ + [ + 8199420671000886852, + 18426707340879435580 + ], + [ + 14176229977620810645, + 2625893583682051762 + ], + [ + 8541415043133431036, + 16289133129889938007 + ], + [ + 15499046450924242968, + 14370346038142192987 + ], + [ + 1485188660735337233, + 6660493963917212793 + ], + [ + 1956219121132791613, + 311027967331965004 + ], + [ + 1503921708020224225, + 11825849495836135759 + ], + [ + 11417146328867696106, + 2297339978810131572 + ], + [ + 13025877441236089448, + 9905545813827660481 + ], + [ + 12093607632807196419, + 14244818556849971252 + ], + [ + 16155195981249629994, + 5423708637230838939 + ], + [ + 13975816612953762367, + 10668528453232724978 + ], + [ + 6080120619943645125, + 507411816698591980 + ], + [ + 758127384540358008, + 11100013908596141745 + ], + [ + 1303977669600689171, + 10776230446365329353 + ], + [ + 3838577941491900548, + 11023167543326546271 + ] + ], + "merkle_proof": { + "siblings": [ + "1261391944066993630372745920539344151260728286488553940696467618752380810740", + "21366687893229135870769113467236432358946224240490701521991316105615992489910", + "18308433314238731763214940036906461950798478025992377004543490659485191479873", + "7338755365571893797622338869037832024224840555083353815486226672694647359830", + "5183385159585300996088192249896769150393050682899610163144963106792551976422", + "7036519078470366142909843212095450641204842977829431736682990321475434305553", + "1415172791413240681077913087235075746255321771166983339670080108771412925751", + "14007624440094195121247165706853957844373153338106633103853118106615019848743" + ] + } + }, + { + "evals": [ + [ + 17309772190346116308, + 6406189199381350050 + ], + [ + 7488401477954252915, + 5094087077983833913 + ], + [ + 8299532570968259075, + 14064914014499578150 + ], + [ + 10476502490035745167, + 5634632646570790943 + ], + [ + 2991471744076481195, + 3738254523445253671 + ], + [ + 6761853807703315326, + 3634831505134245989 + ], + [ + 3189470750376522325, + 11208557619516842237 + ], + [ + 8211863385703679917, + 3204563583117724666 + ], + [ + 190223806528812920, + 16247206546862523491 + ], + [ + 11766252568128504316, + 6998337259259016879 + ], + [ + 16308650299141376948, + 12586435584943121701 + ], + [ + 4738557710231196944, + 11930609239648744003 + ], + [ + 13729329215944650206, + 7789904734226228429 + ], + [ + 2976487487710505008, + 17553114778503294640 + ], + [ + 5404997963319081335, + 14459024799257364991 + ], + [ + 2629880008587676832, + 10781185550040235148 + ] + ], + "merkle_proof": { + "siblings": [ + "2097818714855059134796037152021797383478224107575209039245071117031283218772", + "14082865728956692244123195914784827991706249006436561417280852550155500664197", + "475741197625023805165999545500117355774520782014331653252984017060322612154", + "184289888923504999742621315664051145043133940116103002966333840498981047281" + ] + } + } + ] + }, + { + "initial_trees_proof": { + "evals_proofs": [ + [ + [ + 10922231594711491631, + 209627314549135159, + 6439293104046204750, + 776089941553953631, + 8006952218987401073, + 12632695069977295606, + 7410024031052963601, + 7915155804442199249, + 11164300526752841057, + 3580852347428805796, + 3400674718898609751, + 9473576088048719406, + 2644577446300340625, + 11907024142939738474, + 16214128582563948974, + 16861197576683861253, + 17688830658691361392, + 12681300995646053359, + 17405237300853693161, + 11559807745404966241, + 12529116735361628555, + 774599190306122918, + 16696721916695299811, + 13733580143616282379, + 383733180535078530, + 390849904991254429, + 3310178587689663046, + 5746720877384380656, + 17300783666641330121, + 18255413227813131597, + 6442949713119551393, + 12494410855762159314, + 11196702760934311632, + 12169451562191239009, + 8023200197539480319, + 9717974027125931301, + 3796410625023252374, + 10169308158688211395, + 3786568216644872777, + 4394468970318553721, + 8659622637137484474, + 526955632634803460, + 7856507756171161611, + 1861061896699372969, + 608645015346909807, + 11556641348082969797, + 16795094388249292841, + 1113249724373497099, + 11005603064474974378, + 1614467289971943804, + 6670323390686113120, + 2995179295658733379, + 3193230436330775408, + 8633372068638619453, + 4219563482848135875, + 15678030943260899977, + 4580272080798768223, + 17874829955600462816, + 16875561541110922504, + 16712658115880635745, + 17345908312766668927, + 17908737020713878337, + 15022650160860385628, + 10300824242338869488, + 5169992807981073944, + 15152513061489995494, + 12256759657801836395, + 1363279261025399109, + 17181228128572780927, + 8359963129412597391, + 13991659047733346015, + 1306685417860100206, + 16275070967228246037, + 712534997533226034, + 18023607911208655333, + 11647579579049841537, + 1080824146023994861, + 18294815450090976357, + 3954957191894197828, + 9489198563551918506, + 5070490278786440939, + 1519934429324054820, + 14882258290683497714, + 5318355704113272477, + 12050882993516234347, + 9738055027647431014 + ], + { + "siblings": [ + "3684109262945142752629499277149290533777116095952160262264603908359404877297", + "9780352777082868476054158167399146868826720478473126146117437054540161192777", + "13293568531577160896376983971148390185424577734579940413136941184969502766939", + "12995507206742519536298626354787013174403399875250203146767355560670290508282", + "11886783378341231116182469747664583205680434526297739437647160919605747647436", + "5812418568434001642263448155637207274166716017177447775453674923132556162887", + "507521749928069854459893483096210200799894407012617148504863247799756556947", + "3353106114524456059135992792133678498826352920876204205129139283263163505089", + "4055234115477484098188090271614426966520660770839665418254464630923417264977", + "21605635132658929652278144069972036735744264560748050648977643661183251571762", + "15884623573975509332529095298580258961380357489486311731615942169507788851562", + "833686812041621136368562782637446743187978419554641708972328081790769960188" + ] + } + ], + [ + [ + 5057510963356131381, + 6963272495492293523, + 9783221233824795953, + 11186552514889448459, + 1121763127598574135, + 4525564981575720361, + 13916716117575981313, + 18418563466724997726, + 8566521479354249156, + 15971021511376365601, + 5675764906103293615, + 10221772135079467565, + 5121682386877575165, + 11136722444236586006, + 11836979153786227137, + 5741685826568902685, + 1107150424584535233, + 7449318284758426042, + 2475483863572964106, + 1402213246188278685, + 3982969756712446227, + 17727138384500284250, + 18346153000229709751, + 13965189802813869403, + 12407379228537881863, + 8212419285882453615, + 15994146991187684772, + 15423142535360202010, + 14760955913872299907, + 7805451505369618969, + 12501725935968837561, + 3416684379769257437, + 13730023879466971734, + 13608857039028914155, + 18315288372382519857, + 8425580893543299842, + 17553948464685090894, + 14424427403872940204, + 9222342835196815347, + 15608824806666948511, + 7373301768797181695, + 17131873470868885598, + 2543451911211644741, + 9916834852992978006, + 7959339457745502758, + 11303291423976215315, + 14585226984431418734, + 15369897385553911450, + 5596154958516745501, + 14225610617208141087, + 2177213566435815738, + 283865098105524159, + 3503479165020201270, + 9047552196467272799, + 2178842069917177854, + 1295476755645191911, + 18034189151082476896, + 4239366508632496719, + 5055114890459967599, + 1791707094017879283, + 3678569042875564832, + 4053422858380552428, + 17440651913798709502, + 15983592986455729555, + 13835757882796125020, + 4408652234913994358, + 5487719397814093249, + 8328449917906906023, + 15131743310757047943, + 12136237063145877308, + 9969928479708996931, + 13621027604854468051, + 14118193226002612312, + 2686136766134118640, + 5175393127333631023, + 8309176818344301988, + 10639290991316330449, + 10590324748745809552, + 13284054145052956273, + 9622527705290439009, + 7515940700380357166, + 10480568390792439406, + 17324111411192553889, + 10285029237456706136, + 8047797716717040274, + 13074295760125694900, + 11584747670437911239, + 5222511392187151057, + 14374202316183679572, + 17015381081431761160, + 1846754717771527883, + 15951684442456166149, + 13555778980854914918, + 10542405343218983246, + 17311275619967453980, + 12108408311573884333, + 9945985992274853365, + 2275723815617506325, + 16251224949939981556, + 14385465713417962974, + 17928384562424254530, + 18204771452033537087, + 17733714869637995641, + 11335511964138134346, + 5195845524595268331, + 1649443345818230718, + 1198611823186681286, + 1436541367740472442, + 371282269279973065, + 4959712238788463592, + 16112805874085188750, + 14036188193313579445, + 3754262915812122066, + 16096557449846236315, + 13059880924339031809, + 4450739487451159229, + 2334632873612375082, + 10164689371051943674, + 2994930699832338163, + 1252208439409470992, + 15819779635527505331, + 4629679122848015064, + 16063426525399285267, + 7212062272373611895, + 8440964307217075750, + 7012949293997469467, + 6182579286834780885, + 6302908256787155469, + 10727566650388834008, + 9726406399676336543, + 9042901977736670287, + 13702420297303032781, + 16433037959187153847, + 6072047864958025033, + 3724549302990918974, + 6233315378451187011 + ], + { + "siblings": [ + "21372764060845824147589455704739776853259393384308725757082599241085784149093", + "7713242850062357815315944834824646091876232185556528812835589598991862852621", + "1049337382346097549212495991546212375227286987859993061511209620595352694249", + "12418216808581712369146486986381967422215871751262491505517073166655975982279", + "4975133316836189038811209630118130343441088866780430318918546428560407064672", + "18357597503688819383098534510958093073148040818195917467702026762630060869658", + "1189543383770105020859833850020392023496227572346871846370382924588405569399", + "20429546047384827425722999464271941296495036635093093932497532886830550178502", + "4324732311476078262847243258648002156152868367178199776328665093400593015907", + "15654797599466780713395260325253530602831677831979513066175756983211864446582", + "9795936623914927752374120084213044990152932816067348158667964589991788223271", + "3667163150166988326584592117399540812730466804950677965878303376363071813123" + ] + } + ], + [ + [ + 8807423014751312732, + 8679242389740044418, + 2339362260752980332, + 2231829792675407631, + 1622368938444947455, + 11914711034346326734, + 2037249811725970140, + 18368846034123177148, + 1570880478800348692, + 17379915103598487743, + 16499924754165859336, + 3155930359957742267, + 13161452896236470002, + 16807799516238697214, + 4164728575126218481, + 14921674079946516502, + 9683698020912360365, + 18048109290365250690, + 9540608607110230997, + 7334538491789100027 + ], + { + "siblings": [ + "15561340720984792562484916711615826008502839370591993222347671787996223214745", + "12469141244395573516620410373723134861905275867095518070374331456953717921556", + "11787367229391772550136004212556444116384545869189151834597741764643841243404", + "1081912960685448313995621687141352606316203594847913024802167683035626946478", + "4048239091631295336012516604415128548397974643534564972579833916752302502297", + "21869661961779192186451876394768105633423509197957674697004540370664942652463", + "1577524014142217121378078074398152148709662297164925953343831035148944960573", + "7172723254561449200862737703778453541024275289023054760741489366912271368437", + "2917997635487122788195932398520764006028166660905400401960980682982830740261", + "20903514010776439854089293623964866573981008012781793383578134965152575864876", + "10253929739787435664728205457123164421189682837749815789211967287318695077880", + "18970132539506377343297585100272269977996646715063798910335391871394293545838" + ] + } + ], + [ + [ + 10894687781323388372, + 96620682592114520, + 29334891796080345, + 11815550230764396509, + 18006181483135849145, + 7926258451372469966, + 11813429974089943624, + 4080650027374084429, + 18095097991069908024, + 10769190868407052117, + 9394505210545038236, + 5962892162165574301, + 3465235494333074912, + 12139510782741957018, + 15875892254429538602, + 9172574654968111679 + ], + { + "siblings": [ + "7102141907892951373997435729865463493483220673191162234406724303184938499865", + "21508618519390003512761266537781134831981840060927431875325539808481434686172", + "17986157102217214372386493488606936545137022065421675642133142092559343654745", + "255970116961302579932506328793460673764648347139517784557341793508313854768", + "17429561480899811667557160960684675637386675031554567266076020625681005417762", + "2726051337545328625525008864231927175386884277550902747277492848864653552083", + "18255239019998504759191083448090519760178657382018985352823487816415038613416", + "11668456754840136758425948934380214366290927451989909399067802984453589644696", + "18101997042335513898303555781201152198177072418729760984452128632640431885767", + "18438167440959524731906742940355648659276400607841016361671299212328665829731", + "17617356340550044697469549822412353586628277117790094942957352785108845446392", + "18729408803597696911071777177593874712371121315935390336737799160920420139796" + ] + } + ] + ] + }, + "steps": [ + { + "evals": [ + [ + 14952403331744689801, + 10838337037370026808 + ], + [ + 16674970867595343509, + 182430210026676979 + ], + [ + 11412364757524110081, + 10067693449819416823 + ], + [ + 9707793567351906425, + 6208084542255205956 + ], + [ + 1308778953515077853, + 18403652303457113650 + ], + [ + 11586312806790482165, + 16398660276324126413 + ], + [ + 8600724686453309198, + 11911007580568839589 + ], + [ + 3948872656453152804, + 16485020398326401770 + ], + [ + 18261565005168238706, + 3171645612158674936 + ], + [ + 17601818646725316663, + 10433020950675886530 + ], + [ + 12883883950691449364, + 73302763896681479 + ], + [ + 6084232660623907941, + 4408166281177843335 + ], + [ + 6133961782685390667, + 13286356505833995554 + ], + [ + 13186870090283640201, + 13584792532157646690 + ], + [ + 7046094918691244878, + 17511755459455370330 + ], + [ + 14863172182719606677, + 3096220786887329117 + ] + ], + "merkle_proof": { + "siblings": [ + "290189970867500427952166201032894820499135699624507276066884827985568290950", + "6866542862422081300994578909056994673705669152093371252061174717152472392234", + "3626827545777578838280107429869491794139358618018826323219759673828192665262", + "14178221600251634061852954945781900139221694132478186559062177772737523333076", + "13436728985324689199202357107602549997700909490246003474957557366098700537821", + "4428662280762332326405315063889005905438402645622993692350251532641224969998", + "1798104523498245888029448160525811341650346416394473580058303185547818226973", + "7305189417671402927784045769569052369425755566480058960815313782800279208303" + ] + } + }, + { + "evals": [ + [ + 10694829602185781100, + 12985302373452887121 + ], + [ + 5647997698585254136, + 10259813973860700413 + ], + [ + 6666359482743041311, + 11586069281742064656 + ], + [ + 4735866478969612476, + 7219132178274417682 + ], + [ + 4168495782191793366, + 16407726465806504387 + ], + [ + 720107226748604297, + 8089073980091722677 + ], + [ + 1663358822350732520, + 12177926313233356753 + ], + [ + 3754375636086147263, + 9356552495201448000 + ], + [ + 4150936201204501305, + 13065716287687432087 + ], + [ + 13727967261426912022, + 2527244386243519542 + ], + [ + 238317763677693290, + 2738380047205525129 + ], + [ + 7527607717271360350, + 12358889298887641310 + ], + [ + 7351403778539097749, + 971813506472571298 + ], + [ + 9932480105257119874, + 1231824202430110889 + ], + [ + 9425121242100634411, + 5042904263193292417 + ], + [ + 15971587236120342399, + 58673881663078227 + ] + ], + "merkle_proof": { + "siblings": [ + "16741534589696163112741994897104337414636502551511963467201765987249736956101", + "3599256453014374893378278976726849225706490538775955081574792352418635042483", + "5528474525533860402765034983565011625295217837411867943055875650255973040319", + "20604967186462586815332117891446805732781900573836202088862680828066421475551" + ] + } + } + ] + }, + { + "initial_trees_proof": { + "evals_proofs": [ + [ + [ + 16310066825033140078, + 9581100213838542098, + 16403337733214239011, + 8319473939334159992, + 17194335507452340518, + 12776477721486570484, + 15245688294260040023, + 4873529277834358503, + 16197084819580990551, + 1217166486950481200, + 10717744610114968368, + 1251695528531090457, + 6406206085396289112, + 4760343444048236688, + 18382842703758529197, + 5895685520024338298, + 13919391290087857386, + 14895874075279820339, + 4599174803229669712, + 6123207120845368071, + 2635853081193623582, + 17688757508037754819, + 16465022972843880697, + 8693931596027461465, + 4811059875150228496, + 4438029316809928315, + 13941579546009444665, + 18304794819807069263, + 1732686339599137221, + 6118082222754764777, + 3650215689114672416, + 11188522013187926475, + 12533077837888999203, + 5570465090081174473, + 4096430071609630355, + 17350926904291668700, + 7711254865511196133, + 18307455008387606815, + 11621773902906740037, + 16423396850491848542, + 485231258402592281, + 13445247671482966635, + 15180034848571096407, + 8666477164566411162, + 12699022457080003099, + 6949159886722753755, + 15258101336326296677, + 15539676501335955760, + 4261398327162847178, + 7647581774527289958, + 844642334596918969, + 17906278300919477174, + 3218779637015010455, + 17734430191316401820, + 13879077889263414388, + 3264845688529098276, + 16313135737996496525, + 13035216489356890030, + 14898011602372099687, + 9952392746300606584, + 11257655684577702220, + 3746926284973646855, + 1344003930807299464, + 11123576732603117763, + 16688470168111259078, + 8982185658051742125, + 4504992625133001160, + 10924316316687658791, + 6138977321353029372, + 2409738626570085185, + 8849244838066142623, + 16402195971646170226, + 12401511675735340017, + 8357175827831543436, + 3322141886706017598, + 4821816994957888251, + 12194357780271161523, + 8884041532548553036, + 2013634204965448834, + 15010225088344098428, + 8238031982819459065, + 8648758989116077899, + 9180103791243959307, + 5840818411781441322, + 12158250193494899074, + 13972340963096215139 + ], + { + "siblings": [ + "12934218788423576279983080422138291676402085454188437655009848182167618596886", + "12141058256239546046598524563248998809726739216554996813920998155681487748284", + "13565221530906499955099315707479723315299211224076498308863920037037038469687", + "1795082096142832383894537403138894358974743685068381076243471674825342209780", + "15124178863713636526034518334158548122123616072600828433037682840703556609038", + "10055307738094981766967709440444136727184392089905520363272399705618306825527", + "21758826265196246496640409509569858485900516364175958398112545966348963943238", + "12527787231263239146008738545181148545137988228427321873816578738182125238915", + "8329960625444031592475364215559294620976762229027830443425226457292555545186", + "8817985656149265115674476898122324831437500643417093811400473824544540707983", + "10278255475218294318100298364953806763859922856742879760629503155430572875500", + "3943223806205387565261884245820203200000801998085528824914106570372128610448" + ] + } + ], + [ + [ + 13225452333041354567, + 5724594876909751018, + 7004608372968318353, + 7186293370620492479, + 9506102840537806606, + 14053463085313534765, + 12146999316229195004, + 4020244900455529094, + 5638282789153478086, + 16045637706667115081, + 17761806972460449264, + 16321248267012774208, + 1074582891265094405, + 920095930685383269, + 15451533244593832169, + 13467756383651359515, + 16480653279166345173, + 47268391898320955, + 6055001152078918951, + 10310878999484334549, + 13772854407463954671, + 3845419294816728167, + 15450807047337190348, + 11544183776269681625, + 4068687262231629261, + 11222368212581041055, + 514008940254331757, + 3228724492877972694, + 12774519386534159819, + 16739276090714190262, + 2617392018854434573, + 3305065827073191802, + 12971045832651557997, + 15982456856833788364, + 18082985124937377023, + 11524130390854330660, + 1659672184538863542, + 698942863876713409, + 1175805104195769181, + 17491840942523158751, + 12470788288957857593, + 625230972109748144, + 14509408645082655127, + 17387268743593678888, + 2314678671267095543, + 11761308383625428572, + 7296871032997114709, + 5795050046610568990, + 12674153758911354495, + 14282573250050719809, + 18365974894533772542, + 5481115486915632898, + 11119379023249407685, + 7867486689676801075, + 7596180696920804721, + 10874351585186171217, + 643508594479128400, + 12544300378417871424, + 12033356435114454039, + 6653588633929774691, + 4996370909062532511, + 5058106208948844449, + 15690718185655821267, + 6762916266790177319, + 1829539897742736171, + 12579790024313958262, + 12854223123348327804, + 16747420084360808968, + 6261534095294156591, + 4368073302895565236, + 10683946294896210141, + 11013030360715486495, + 114122407992730770, + 3532377769474211350, + 7144116397958007657, + 3032080409218799225, + 3981159753895386582, + 13334883885253702625, + 737814092781413660, + 12126105845941604167, + 16319285867019711953, + 3156672025233741379, + 9526565895829736707, + 9138044315085861026, + 17922499217366826228, + 13911979755107467878, + 6622655529518393240, + 12519955015994666198, + 14952354855122933354, + 4722394523242663679, + 8000902711980103355, + 11521579163528410208, + 1808995716492012573, + 7096930213799893793, + 8022907486342579193, + 1621389740351707570, + 6905162320403612845, + 13333720717885324818, + 3990412408860001667, + 5511390191008131610, + 14740134770565597518, + 6889937798606076576, + 4666298353917783542, + 15592082226686296794, + 9235533404647115483, + 15141813006470595954, + 5332621259630579887, + 12609037954268385666, + 13268390776705515750, + 7312449530565792073, + 3943268316124899148, + 3270531418732705218, + 12322576755625212310, + 521528326632274687, + 2110143515848455786, + 17897917658720829737, + 6879812811621470793, + 6228455404343645018, + 18315752968017283440, + 12264558275798368961, + 7257440519052374337, + 10882499368228543971, + 16462310943590681355, + 15813581675495872667, + 10328930890981234679, + 8965419189660531549, + 15182000005075420709, + 14939501736157176076, + 5854421085905897397, + 9871878019781699018, + 5003664040578534134, + 9719712690459676455, + 9139664919697527696, + 18430570171781591653, + 2521000579738644670, + 2857422777650983604 + ], + { + "siblings": [ + "20048086678793061859369640474016292387621203149077860315496544819832125110117", + "10844034193230702925156238330087382748356527696191214938197958752300427482152", + "186288072349499650324616378231996925082663550887535592157379821149263285774", + "198795181728958209226312011066941709619500483808364879053813996651235246948", + "7991847461676525829811590329748952050875483547731665445496577024372650570165", + "15550312311446225471837322216593120850685885235082957175143812834038690805854", + "4664808747061339875539452096246279178313230239985292555432613867556809104520", + "20124477213272468514256930468210374182438209830451681970525790219853820424826", + "18944183333222943077540611029647742189574305580775022308779464156920438655803", + "4799422675038156482755709438376922315970650800273777740429993500897423863147", + "5914932830096405212831898459163048690408709241931647183554895472872663173145", + "15467918673994982053550828190955269804773939308877788420927932615579634468989" + ] + } + ], + [ + [ + 7154898896475910809, + 12499745044832220966, + 1424633617172611310, + 14279972171332957265, + 17791060544227671061, + 13879237077683033061, + 15874196112299820359, + 15957481475893367128, + 11572669788003552757, + 5200264842467617035, + 14372824828728309272, + 17134356861489919171, + 18248040870975393138, + 8686026480849621193, + 9913063399638867019, + 16222227136313427276, + 8203733808004783789, + 10111205364959267988, + 9437380738173298776, + 8811555792657924803 + ], + { + "siblings": [ + "8886916650059530041876675021144880527274355801386691517433738080622610915486", + "15621901454949925305908704205062473167867821913177244126264420850951345181335", + "8803517427247307385560587326845897120881093781795523284413847834927990609075", + "18722588758235206430328890640457358592066202941155376387122426377941578782176", + "5245151740012423717934192556400665050582804618856067387803796687717136001765", + "9648671870874636334614200167870986459460507295088373600693027538865572846746", + "18871862857749077017468529311497731129993407935298523517909564491159038953584", + "7996723980703242557551263809288367834094340422619250043190846861898522013252", + "703021017580699850028335678188640865511107149361964866379567849128577221011", + "5232488405456945515661487665125215812101582461128896207451146252495670113497", + "4788248305406691269102790876918320951802726265923473143166463188395914845398", + "11308713699120728188143901013490387640158701389272044016899264971828216047131" + ] + } + ], + [ + [ + 1432940793164819847, + 4894210412715777842, + 13609185894499472918, + 11393649560497098839, + 5386909012878863348, + 5935002767882278746, + 4839072409335915833, + 5393319302490640645, + 17595875360915920425, + 9779381531784065093, + 15966229067222418738, + 12665729783215146205, + 11077403208385558961, + 11930271413605760583, + 6927534450898901423, + 1265619106877335929 + ], + { + "siblings": [ + "10215819498719924196304549525103914426581405049230532011383272341081797827525", + "17879366197715263113873250533916403861317638926481054068336047616160588516922", + "5595930367697390805997009983837044591255889259986833553067818495895441364056", + "9862035476934536291578913225085070300038865133452050920768289999860310258160", + "12432233280340396338483812542521724507422993436523468704281800724427517173464", + "11942355910812681951324964220866376590002065911486935461673184393906447538645", + "18775463289150255380491072320071290950222327487453454349708769433558797859463", + "7930558841135443550808862674007425538335637860714983900029881875572249274268", + "2177437747083701732711365989904105581112419644028332353683806905988672416575", + "2518277530958687728279081127882280686578049176829864121766277642149656708215", + "21738929391840252561830170367663147681175701165873306865355890707023207696070", + "13134809975533553744613862441494715921248642999826375363042104015294055548831" + ] + } + ] + ] + }, + "steps": [ + { + "evals": [ + [ + 5742906901182460106, + 17628470252432971881 + ], + [ + 11399236577949537876, + 1291065824197646764 + ], + [ + 12036329072699916129, + 2270056364369732301 + ], + [ + 6738739632849588491, + 10640043633701091059 + ], + [ + 11290890931262543783, + 9214799764262699826 + ], + [ + 11093580462132453570, + 18226234795141378089 + ], + [ + 8301173880770844243, + 7356496549474915455 + ], + [ + 4093624910698981865, + 19165679979099254 + ], + [ + 14091675520125949978, + 8915625173817741980 + ], + [ + 1997142888850199570, + 1333220381727723139 + ], + [ + 12817378362479270292, + 10881711793562504315 + ], + [ + 14157829841111044783, + 13429758469168405704 + ], + [ + 2909536388984577552, + 11670973113508208135 + ], + [ + 16402586062935642692, + 11076536864845123257 + ], + [ + 6293714262569228122, + 6847404890210318497 + ], + [ + 14675621510068858399, + 7065655743036884982 + ] + ], + "merkle_proof": { + "siblings": [ + "16823260513336179324972355871304385399076591175213703984640864486540970160952", + "8209238863456725860640006900799462826008555337895197588958152129187722267880", + "5488428723285412311066792277971889423521688251794176512009851276129384227703", + "10090912255024776797293240382232704860483892119957319761787946999281832212863", + "16592016208506771517151118490655472694683163763777637827291429125542549292524", + "11015311059978992845902890803839310365988530223755418565294023010660191538534", + "16233927223976242383733209841388085884076071696756457410089487092210923290939", + "17065170513986761269251339943257825357932113864861342058578383110251167617312" + ] + } + }, + { + "evals": [ + [ + 15192378008280371025, + 18301092891990313589 + ], + [ + 3774351124035893872, + 2624548935427978153 + ], + [ + 14378839594879226312, + 7646949685633021574 + ], + [ + 17386124169776728362, + 9955402843011679109 + ], + [ + 665300401069998573, + 10552871875409591792 + ], + [ + 9895871592461283054, + 16581392757110334215 + ], + [ + 18399915966471515232, + 12813229510630643970 + ], + [ + 12174646790381869049, + 14915305214834453962 + ], + [ + 5882365930855961735, + 10705237663698612679 + ], + [ + 10312431692333947946, + 14447423690529506585 + ], + [ + 14736823144750768548, + 15423113888436490138 + ], + [ + 6763310407699349771, + 14202415198953375897 + ], + [ + 9561619679600526609, + 15670631119545900266 + ], + [ + 11684096008116404134, + 5373669807611199659 + ], + [ + 14072908605942902207, + 5193027976679128061 + ], + [ + 7378020565081503421, + 5770349845965039765 + ] + ], + "merkle_proof": { + "siblings": [ + "18717183145106614344055074001528187148512368923812057099828450519129359655020", + "14901410758582438862704679950632157854029120591938925182080371147339674215756", + "14642836818036725749896270454920952441748485653638932333642895746081673273564", + "7104749307991784933672368637677412263236194695488072538662793228379316584994" + ] + } + } + ] + }, + { + "initial_trees_proof": { + "evals_proofs": [ + [ + [ + 7025096819390179607, + 13808515397467881928, + 16494165025077979491, + 3967735382397018176, + 2472177977258501816, + 12235051102201310229, + 16165570284749133132, + 2338120470076757932, + 12526459510695348744, + 3887815546439804368, + 2219725212193554267, + 95088709236647879, + 5756937610247929263, + 14140689396563081560, + 2078976355097358926, + 7614013836116633370, + 10175053691456334586, + 11739767568008715785, + 9914121037967729639, + 8214363853247864322, + 15227543918470689808, + 650536042627115196, + 8956326092768086397, + 2031524173793854368, + 14992746271301863603, + 17365156769459650170, + 9478661622059306074, + 8608108352353957405, + 8284455499650576623, + 15736909981887906777, + 12470946488484135997, + 2310894482827116838, + 3019650300706379427, + 17546339871038700284, + 1710818876023845486, + 4938068155138280192, + 12459668225340028640, + 14402097200021825345, + 6462310804074881466, + 13790777591757437290, + 14513844944816848121, + 2099499087844453319, + 12719682435754037673, + 15699299349215041431, + 10481383893831629492, + 4463997206148855793, + 12160761826966567765, + 4019711225983363237, + 7764349807233319562, + 3263615736530668304, + 16923026898449529364, + 4572874143244249695, + 6072728427620153964, + 2669815948716173996, + 9066555133662001231, + 12184757728855670305, + 11131519529296037577, + 3539608971584268633, + 476835950758366696, + 8448953907390872997, + 10494397882916837743, + 6490007041592286604, + 13379728572486308784, + 279361931121496427, + 7162625652481134765, + 12065861908860925856, + 8566187440933063116, + 9678702964893348150, + 5667061664521589122, + 10919392755620070079, + 12375533616067785236, + 16194200074521603278, + 6207765075838599285, + 13314117441080583172, + 16165022992093304119, + 16549173826385809611, + 8666540260189325224, + 16093596271434034164, + 11289821812416108431, + 15998961173777492342, + 3453892034328366698, + 12962242660899293442, + 11566720246770181683, + 13416919379096956801, + 15525050596524333558, + 15720997044580971042 + ], + { + "siblings": [ + "16035609161109081342613336191592291358125910118947314240844339705024988797759", + "13505824349253975186322289942554106380426284099470257911455476813107321197027", + "13746064835775584541657537099230422280950060989118830469243680603714791375545", + "4739970320086124972118372515105391657624699417012284459173376711108907409522", + "19319120295071708867339226508725817314538356524892057691263132878126689068229", + "5226830547025829930321537233870149595483019890149810512302753315846600523788", + "13273389692304166866523043796326942006046157415998266085974120020532606359853", + "11540415514974917547386056373852270437721930219400511403812144626609013212303", + "8171830950078957566642946984315278403026818108687852971838064835771099760745", + "12308972361664836530847032347033811074839700231696001228934692481883323212072", + "14790866537153301742104832383429216495644393732360404271733140093406907334770", + "17950634223319622329704731292629967195651718825833605390927722496175392367218" + ] + } + ], + [ + [ + 15074438565218604471, + 13139749801584288402, + 8106416979142851809, + 15834315117931693268, + 16316995909607635439, + 7443490186458785771, + 5066561178927695305, + 5347643987191637937, + 1682973871919443567, + 5342358076318813000, + 1813116614217843022, + 16215594315479846452, + 18246642787837660249, + 16278885231571810888, + 11442026179356082181, + 12706509174764083030, + 1685691540468612823, + 62781164965959674, + 15210394479114121637, + 12402957813101731729, + 8902744395969654204, + 11006127009393380714, + 2433862641815361014, + 8711039007547068640, + 16779642846970647528, + 7846323594795690302, + 6051589360230944828, + 14376001969780180622, + 13839729463131086186, + 13330124641397935511, + 12476921080611203562, + 9521999822143136594, + 17393299852336697856, + 9849583185593491919, + 15633283759502528003, + 1481268067106677901, + 8747642899186093419, + 8480360489803145355, + 547699401333082205, + 193765031712650831, + 2221848759783728987, + 8716427509576855161, + 9141907819249012564, + 13397480061053799017, + 2470706400491750576, + 11639928452766368025, + 12342733796250627645, + 2765453811334853618, + 1739706899515512140, + 6234961482555241628, + 10718313874205236030, + 5481509402179734408, + 9292526185457619581, + 5820511365779432711, + 3490653170116857578, + 16058269628229045634, + 16366501774663746321, + 14823986506193738489, + 15915585143324664735, + 8640886251515308603, + 12790201041078993303, + 8293633246925157115, + 6296450278369094660, + 15696364327121255819, + 3572391932024611333, + 13787006979557817028, + 4725447306460061023, + 1872255045797796492, + 14455961087924740202, + 2970142814520278401, + 6016967753412379906, + 9201112645422530133, + 6557822951961605310, + 9554822880414834489, + 10926334594927266009, + 14128760932759377782, + 7665557447989131261, + 6618666142152564475, + 11196201244792737301, + 17095112694581844230, + 16273615992369519625, + 15991024766815883914, + 4637721971776520827, + 4979704055059233321, + 1367139078044374477, + 11822137466904208426, + 11462231804935222995, + 13494328088501325999, + 4058123385359640146, + 3959022759976237577, + 4363388247862042949, + 9207313785427113777, + 16423632938973517577, + 3523894741358381083, + 990556731984740018, + 9288241940744719120, + 7339354344358716799, + 1835524032551395746, + 8991762798796316949, + 167964053132491525, + 15690350982598196793, + 11700192569893014508, + 10884427988613491767, + 13897809631594027461, + 4564829314272364533, + 359349934760013965, + 1758402922429783553, + 6506546755721187078, + 10491923637417563428, + 7371694604664989688, + 15498161458267462300, + 14723587295717317198, + 15930003174788250837, + 8406981161374105212, + 8612510705756822420, + 13240865741744652423, + 12948323383139912320, + 3450455192035394401, + 7738831279139233989, + 8716642062790944920, + 286044927716883073, + 15100656913421117129, + 458919960839594502, + 539204547974850515, + 10459730517098597238, + 5836610727680171258, + 8699863875191067006, + 1924275075833349847, + 15214939846147433980, + 16112376814907764853, + 7019436421928295494, + 17726431640286378812, + 3135734845117258567, + 3439014124855917437, + 3089494731307258156, + 7879494939216993144 + ], + { + "siblings": [ + "14689827906548664283318520104204869318702168857567159936269670193551439277118", + "19743705496751039694476287178985015306994647996950235319882687704693682443178", + "15084617734993810465566683458128835065210390024062394583593314969614062625106", + "8830354208451980837734060874582221655216464723930366337634153420373591410518", + "13553208398662340785757659737316304004457768421482469808610086378600945529567", + "13554935841885387251904104912692327359322112961930505878723404267188581634931", + "18565239569859367581288734001599162274474780612074205915288909092093035953483", + "4437304606378770246281515994919963547943748517127707288183632346178876931863", + "14033947871159666366169864224015849813717981851653778826793026753636728112903", + "5885144547304457011559554238156908835380200699873655820231555414724008558869", + "11129864197318451568779033932899456075749727848542960271538955390154766635147", + "3636581569219531739912161427607159246780863289792252879860210922037232236105" + ] + } + ], + [ + [ + 12409784623802125555, + 4264007349240573784, + 7007457981648106637, + 7656589343138225189, + 16047263271369679368, + 10857723145051058442, + 4413008847879445338, + 17978512186729525673, + 3390444828653616713, + 4674355223717883000, + 12469247071329560739, + 12032687210829768974, + 17121721096778194940, + 175028031828477332, + 2839877498396214165, + 15309403059739417178, + 7852154654699682625, + 5516206882151730367, + 1791961451231372489, + 12866255325880611159 + ], + { + "siblings": [ + "16506846446004237707599044678678843944723695468770373483907046210605970850806", + "2146722992185006387221056843150215978452617518361271819983847406270768911252", + "2228040061085527846587786630578502116404135098915894425752611329411722687277", + "20999413746850525064981652115221660879879942210261292768457831715927166450619", + "21319394960781808149719537435888190546499349345569546646827708005045436795848", + "3047773910723731728373559926391357093149341269298836513600725517873194991168", + "7445417118224183984330526177347780291870136673655454236040399488015195441457", + "12500703532455359134681684041409990288313334508486621338044927294689264253072", + "13746369532047908092116397886718931238128836618742521650003575548644009291413", + "2224665737676935727089147786547596277105944551611035084689397501458860810275", + "15567669159759363608065750934779267437804507982522508629540007305620741726809", + "11727423774764093614628294043328647616845461390676350431594059447461758141477" + ] + } + ], + [ + [ + 5382665946236681568, + 12934113398426956175, + 7100190792925845671, + 7814629226775965169, + 6265758105431989745, + 13146442849388696464, + 11123718001595678678, + 9610127890204215784, + 12869907287223410660, + 16820493160376542275, + 9428758693448965061, + 11381025368344038735, + 8575955708109262646, + 17417872394800463834, + 5638234148101681946, + 10958774065611313911 + ], + { + "siblings": [ + "1088425074754616106287776421075285126930553682694342660037131999469521871449", + "17737154926339068860380284304451027564868896018397458201008872290373572269721", + "14463886033608422031655065480447750175094270907606377697787681138112924376481", + "16589070181327671296705582233769684238332185974295203956775649948572881167524", + "8285129201282392943203913146072638225855830191108760127856049300829837104324", + "654023514361665147447010346766534749089242119458933199536247949803090780715", + "13532171400841187802072431639471175613393581511152644331488653960023359465176", + "5825848131280010442628087225078151018725412785391212538840874931414546611337", + "15083878512604043489374890483562142918272787061455222834938821107768364711162", + "18411016871496010133023685655268168396107337784932135065774444082606813177022", + "6523303440334037387409038616165614737764697908953778855127045340261474146644", + "10594202422010032864593439952098298620708873344624604945378076356207537101989" + ] + } + ] + ] + }, + "steps": [ + { + "evals": [ + [ + 6040962850546464408, + 10754085013173103924 + ], + [ + 5776693738368587513, + 6418574616443610705 + ], + [ + 13574294981845860031, + 7843448274299309490 + ], + [ + 3120138725357789591, + 1438263520987616763 + ], + [ + 12394355656979190375, + 6687970024527163051 + ], + [ + 2717083915294873319, + 12503929512253138390 + ], + [ + 6728344114723566649, + 7765606887926562651 + ], + [ + 8355553912177041575, + 15820412958238115371 + ], + [ + 5333704101556665696, + 6991080728985676043 + ], + [ + 10479356569445791906, + 14649935743100518235 + ], + [ + 5012663435655094544, + 2671454400975910425 + ], + [ + 10862614906689009846, + 12683626841758142427 + ], + [ + 15679914165665141597, + 15967184777551083233 + ], + [ + 10481487982937027409, + 13948865088381615566 + ], + [ + 4239434658026093920, + 649600484010305134 + ], + [ + 12482908084971109324, + 3193980797491510651 + ] + ], + "merkle_proof": { + "siblings": [ + "11895198137133639717765130396090900812207019046050412429428680893067648974659", + "281409276299082776317005089573953061226778539053015598436697611178091687144", + "8251742503621611693072141775963263494848976634093363176711664874946396145504", + "1897852053609407760496562409348801350880879013704339456188341774205984640821", + "121385759892408975606609724564341947107911022469456729420654723513903253290", + "14603291166512554958021725360157480395128669120053754278867026438582847814144", + "13810803587131434463501260849998707224683751784444632564877911214290385778048", + "14349890324297666163526616088635582464619401599904225586860293609527870241067" + ] + } + }, + { + "evals": [ + [ + 16878761966900070142, + 12252393909901193392 + ], + [ + 15519919178204530553, + 6120857821640939840 + ], + [ + 11095881092997408577, + 6359081213576004015 + ], + [ + 11753998479868241134, + 2558089015840065852 + ], + [ + 17153469366552150274, + 13853707947409664752 + ], + [ + 2457732767069424245, + 10501393986648801466 + ], + [ + 13976974872964001981, + 14867440505559324355 + ], + [ + 10323612228779380053, + 13191751634485982231 + ], + [ + 4550167943402791108, + 17017891034823836530 + ], + [ + 13679663761157988825, + 7078680162323259100 + ], + [ + 8311193875969337699, + 10926585636700248465 + ], + [ + 1470761757581193230, + 16234728161545139987 + ], + [ + 7181973011760536637, + 207758982971960434 + ], + [ + 11522509548039121333, + 14639844350865265936 + ], + [ + 5634730968520751957, + 15159292023381347151 + ], + [ + 12870591534148370476, + 5758328397829835781 + ] + ], + "merkle_proof": { + "siblings": [ + "14982428844008870714738796726761856761842482827926350309355819287035640669791", + "20566937473345273616052973397947262593091873550305540995460729088956399938095", + "7597018127751899865320412624422736732085806259456237163892267725665121830284", + "6994498322311443900363168998981388864440163005004019159867196268673969759353" + ] + } + } + ] + }, + { + "initial_trees_proof": { + "evals_proofs": [ + [ + [ + 11947557719500630892, + 1371100462865817786, + 5295793814866006638, + 8475531050267944186, + 17420738577193666310, + 11143254217639496642, + 7940600559073637611, + 17170296251924808164, + 9704726365904374439, + 12208311120872395477, + 5799951153491723745, + 9044523980611263344, + 2912210248473698918, + 6101658531647052518, + 7958520997636472521, + 17656977430829005842, + 10354479341751129482, + 2415436913086962543, + 2916956402647523438, + 10366346992400615765, + 1454302459440448644, + 2794271834808963903, + 10345169862262240060, + 14432496968173258956, + 9726902618643914030, + 2115471676978865698, + 8879358836310964947, + 7874609308989892622, + 7701786064529819509, + 10004392297316901589, + 4156999768453401799, + 14499096795429591823, + 13823691774733941646, + 17040885559786397273, + 10327274048033070451, + 1107166770031135094, + 8998262119810139910, + 18067406437603794580, + 6089217860886301803, + 37718054428517050, + 1493362408444104549, + 14626320121025607299, + 14906487733032184399, + 3500600565114405047, + 15130448702741519029, + 15307922054777774128, + 7408470572152193857, + 9201305250946707986, + 3956706225504219914, + 16837677869094963853, + 8580311478298462229, + 16521852032028408912, + 14837866999062464035, + 16814809167252108298, + 4095577121380673288, + 9517644652326061957, + 7644092555411681731, + 17060476039028652252, + 17687389530303781244, + 13929434201927073944, + 11222070775251190066, + 15125139612437739541, + 6521807225159486254, + 1993871057591659383, + 15850685995942146875, + 1572492723394236754, + 7131099453132979071, + 695680784208434426, + 7015411100342782397, + 10148404126581908160, + 11097685798375140356, + 6563133647594581922, + 3730618908723563903, + 8187523769259301581, + 10506369814406687949, + 8083883002053677102, + 18228805783133641512, + 4185637664050314265, + 4849229283606352921, + 15817082818864007712, + 11239427014963695798, + 17725641337252400391, + 13771994784581278064, + 6690660812196710249, + 17136583632634605784, + 17373527925914795155 + ], + { + "siblings": [ + "9962612247343301716138011263959891829734660992487556242944516992944655689530", + "14085616349504199877791007789039782785008676120113740724568651054367520801671", + "14368466436211976990536240359858968315899109743798997922746483911851868155633", + "6247748028637040160218311385166442599368775031420667042564296680792378456269", + "17100917249083447894177569833586220792299965228623534030865643428638086348848", + "16471789587045279056289341426305662809193482314296798606657560777234567605517", + "12456239546022373542374848295423832301781677334453583713910491936428412571899", + "9222895714581533315770918759198953640787112761103494491792989514287028927692", + "12306740169722242872802001152378027889228924885656405979343854835276881868645", + "284967830836839803294148931243543146153982571949807781105917073032386627856", + "12736929604358786654887240128129534179478449994482395792116547262817247931780", + "833686812041621136368562782637446743187978419554641708972328081790769960188" + ] + } + ], + [ + [ + 12170932003559074555, + 2390441714624346663, + 4775808127358101785, + 6401200408161164447, + 2164293099621470541, + 16629446763899707956, + 12310318862451031022, + 15969377293944724395, + 17070411504564998559, + 4929372279903482516, + 15182332714566740892, + 272306551990961143, + 7973329941056730127, + 2065646570105518953, + 7240080625806862834, + 5445641384242814992, + 11939405190111921844, + 3138034643895675531, + 7029281555749475049, + 14680451018435676687, + 14374586452135240952, + 4519184584927220067, + 418305318201985081, + 10317553244910008085, + 8290806942416273701, + 9720810019477950123, + 10241435185186610645, + 7183531316675344153, + 1497612420163276377, + 14283921183180138529, + 1346898548514437285, + 1734895128783902859, + 12467496339210748949, + 12293770345118007067, + 5095478314829064594, + 16892858035292531892, + 8067259790992661137, + 629119014763587502, + 4171057517498664272, + 9308009703973101321, + 9009233934573624338, + 7380226835042442977, + 12172369087956324112, + 8865028107292065571, + 18177773923586509244, + 13287499344869078414, + 14303876948779261713, + 10388871595183707725, + 8413790968985316493, + 1775183455724689848, + 13144857108748604467, + 14849918610649824684, + 2162199690805812591, + 16406346895503105929, + 12576650816476771713, + 12553479224735927245, + 3773514672157977622, + 4599242514186121450, + 1186319649043593965, + 365052389670892358, + 3098047043561872024, + 11387185054764104102, + 13716332748309973150, + 15498450763024652446, + 7113321626139537196, + 16320591375573056169, + 8315622081601508585, + 10671250875081690977, + 11643189881299703970, + 9304144488045639055, + 8610030337591644501, + 3587454266501208415, + 4820019574565905870, + 976560477002874009, + 11149573596123234282, + 13382739686549289390, + 8031846207153414889, + 14525322720990661273, + 3681594740919837246, + 6556071165418258109, + 12863530305364922888, + 18129001243799952002, + 16983241439897282980, + 3336259155620825026, + 16895446887528567891, + 17382076519389490682, + 7362250182141537890, + 11522434245866706055, + 4420950638833583061, + 17759533340630434495, + 4390372010303517521, + 969229860002753817, + 9170533753243760346, + 6816496785388679264, + 16167558227243427406, + 3644159104490130474, + 16058792599058089476, + 13630032859891704753, + 13810735523424323514, + 9677429691933014482, + 3030953760904248018, + 10618356569478977303, + 17298972571331038141, + 13919605124192543826, + 1289888297498294274, + 4606384291725335297, + 15761573018689763462, + 7180685573997918139, + 6300052799170598074, + 3339090934266325433, + 18111478757539963315, + 10273490919204075078, + 473626321120455223, + 14061199234655182642, + 11890702488753922885, + 4444390410442338853, + 9217156326284723226, + 16980568702146199615, + 18283226932121612201, + 9942442337687322156, + 5523497215210564399, + 9051897693746210340, + 17163608524083632280, + 7256434490955116, + 14277923742826876414, + 6474686392942548892, + 15978578206130070743, + 16933957796614580626, + 7600326968938789503, + 17298203434883670567, + 7642665625718938237, + 5698760340263546313, + 18217450660517269144, + 5091382131708580284, + 13325987854819684722, + 42730124823199057 + ], + { + "siblings": [ + "16941759017846743399734769691759439192807205746618365892288370876967402628439", + "15014679166371750228416732906764117938885361474002212199909044720366956554400", + "15664866906541128692837413825831619763887666414969521688888038773140185346266", + "15921410855871326654023246406229852135852453166894844336944767390945122164309", + "21703442377960612953323501225495827414471397160155935604778380033422038042303", + "17895458550951714641452696745539891157920338811240652548649137118292646052314", + "9538425269409981211167407113380406480326119557596482088386044854349661675616", + "9606338316263458199618836299035714357360799648650244177018983780861849966681", + "14179429170420852398839591862552955542836298393040673869968695843801803448648", + "9653284471082355289839778078815052337393885428744783280535017381367491384520", + "17975628349917914516507278588120659938481197186897428027787565136549094070739", + "3667163150166988326584592117399540812730466804950677965878303376363071813123" + ] + } + ], + [ + [ + 6898279025703002634, + 9921998802854898425, + 10921536983211525453, + 5830417487156023564, + 9859744783693724753, + 1741133814692546344, + 9097022736692097938, + 14128066118449683025, + 7563058543379325562, + 17091064816829286688, + 4516981061983629219, + 13792702098172874022, + 2466460548686891467, + 12846760721231653635, + 18355469649798708023, + 15523965328759207354, + 7073504596932266503, + 14915457977288572720, + 992158950329621206, + 15394404010769971994 + ], + { + "siblings": [ + "16487873785411255921435779648387995126779665851161661636969330153690462516807", + "1695960557431062289229203691460379968197351532673003960406911206597576737719", + "10838795654651569652659249342937532514562083075448298692599694850328193823869", + "6686911566376590878436656963042915891932106817548571407281029571122932087234", + "10999551059407213956026536073753796829792233480261804221685970443180745185588", + "20605604248872505158955292191106035293056255879282026792781244098319729460453", + "7576601856447731020328422459926290220385628282172743097703109025590621853435", + "6105317609874592101686852531670460267580470952654494992842739177632410489728", + "7869554736232131505407346756655959132095266731608695308763179356381278823274", + "18634906684776502416378739885847637949692424089612758037049695229339905576877", + "543519091260045931186584003115333400185294886895473775226732948180231885742", + "18970132539506377343297585100272269977996646715063798910335391871394293545838" + ] + } + ], + [ + [ + 6748452663639632114, + 6518980113016821381, + 10730832060600118050, + 17742187964267835049, + 10620195882110000139, + 1763913834649282990, + 15140947327080812683, + 9955760580673147817, + 2582760747549889865, + 8247974927383182942, + 6379801930115615292, + 7499379262047977267, + 7385653815566244782, + 14078735561027726544, + 9235652466578539224, + 1875657077725081712 + ], + { + "siblings": [ + "6603290349061012225904397729357718614161547339063160869729029927878882093739", + "10922937678473853209340409947208964647304606931387746562168606705226892841774", + "14768016324210367017778449446175244692088343449105811631181514763042560983418", + "20918606784292994289572149957878860514101169464067833474064803102518254042563", + "13524459108782891164445184687455392328860704131148208537956502444790398601209", + "8731528023365285419079563659857480227279951915020372591108538391687558415577", + "13521166697827167029336048805542678246038949742791027170677914664785421752463", + "2436742662534325201937888360335063722814452636868679950510577351951365804067", + "9367043474883603251761924280407854951146668980673469876779355535519471612196", + "4170795715559349645814937881158443561875755434205662315365203290296488718858", + "13545634202684850587076594051482250397810062045487213080389672032087309836948", + "18729408803597696911071777177593874712371121315935390336737799160920420139796" + ] + } + ] + ] + }, + "steps": [ + { + "evals": [ + [ + 7781100777602726804, + 13309295024916999279 + ], + [ + 11272108810194293005, + 16775741949485106609 + ], + [ + 14074392971901421301, + 11718960997847288462 + ], + [ + 728282156593685352, + 6756581597710251128 + ], + [ + 6110523897661822586, + 12912749509919840720 + ], + [ + 614460907001133134, + 2858862839068392689 + ], + [ + 15834849369515098259, + 8230679087523003090 + ], + [ + 10987945421824889066, + 10704912594303868544 + ], + [ + 13875482806418292160, + 10580711614338006033 + ], + [ + 505680520260699631, + 10077831782124444428 + ], + [ + 18263505979930534376, + 11033427049241767315 + ], + [ + 15892108317118057133, + 2623606126359170986 + ], + [ + 330811555810348129, + 13886868387639393886 + ], + [ + 3078690796089361805, + 803095117618430832 + ], + [ + 3679443112926802695, + 8020688854881349610 + ], + [ + 9270534186790772457, + 12078318708142733608 + ] + ], + "merkle_proof": { + "siblings": [ + "3822514396910592690061686976295508381820840784503248980521587246009694411174", + "3496609101127574653993605544506066928616544630188991179923073942568252434660", + "7530539752898565798814667174351191796012009967095414326153479202835304524818", + "12581143774354222637710469095712596185272024637755009979653802659781142322029", + "19619502685363632118043827192896761485603913283327070046552265309312610262176", + "14103153438663365625575993159515024935011196322537765483216993149646508566802", + "18474768611841846063866475005463985938168004276426844729366365966559919609120", + "7305189417671402927784045769569052369425755566480058960815313782800279208303" + ] + } + }, + { + "evals": [ + [ + 4092912622032487980, + 1428078146268194035 + ], + [ + 10500493782968668341, + 16599585865317639306 + ], + [ + 15471489105425444720, + 4870663624863963955 + ], + [ + 6228158150905309331, + 13757598337135777402 + ], + [ + 10679594334556380743, + 8564029364310515610 + ], + [ + 583957668137816792, + 163125481952975213 + ], + [ + 3457235867364750368, + 12523809468105555896 + ], + [ + 12461709605485367602, + 8640490452447093632 + ], + [ + 10680547224239995836, + 3334800649613992974 + ], + [ + 9561334778609249750, + 1381003065457070421 + ], + [ + 13892925683708934571, + 266950506167087488 + ], + [ + 12532655479774367095, + 4768479251643895510 + ], + [ + 7943081206868857511, + 13512376365423598948 + ], + [ + 13116460881931555770, + 1689368797780404504 + ], + [ + 49080032863269489, + 10874623167681068830 + ], + [ + 13555976255476312790, + 11115676102241244520 + ] + ], + "merkle_proof": { + "siblings": [ + "20593591464194204048110238529824963185239283989281732428413349464154574998089", + "13910224394348377534373079524834308264791903747408563246595230509490892512151", + "2971338017448880788152506145047188549903636292677066897423737810490532529473", + "20604967186462586815332117891446805732781900573836202088862680828066421475551" + ] + } + } + ] + }, + { + "initial_trees_proof": { + "evals_proofs": [ + [ + [ + 12930420765028503974, + 15943961827850215658, + 8557065324287231302, + 11570041466317681204, + 12535835503086192498, + 10117984499987877714, + 3202022296087279780, + 14367213347069746258, + 1451809779584975507, + 9933384351432706960, + 5466243913268578324, + 11655238343140202567, + 14247848968907528882, + 7504574423722792248, + 8016398628791261408, + 4878953298897184442, + 11441305354771923119, + 9523078208238902121, + 18335832838389492366, + 5405865316132280094, + 13294430163312177650, + 199120265272467876, + 3711018541790785560, + 13877525567366247921, + 3013975716913024816, + 4539433033316335260, + 6128424668890898990, + 2181226890813521043, + 3960092315276653645, + 12426828486192587374, + 532414574525133914, + 10002597930426209658, + 17459299802575163095, + 14834084662247318203, + 5186929379915084530, + 13407656156120154567, + 6659291942602075765, + 17798105324533307851, + 5727928458582614092, + 7835592530264727462, + 6884784637644536772, + 6979064541493236632, + 4023118783747392924, + 5437387259418056926, + 18076810290874772122, + 16097425224196220265, + 5773236845743421616, + 9400119372925128761, + 12538186049668330203, + 3497063870041591464, + 4479477342198896950, + 18363581422621228999, + 10172391436778615654, + 12586517264683157860, + 5121263595521340655, + 1510270552211790729, + 17387208888484562381, + 872442548862544807, + 11735239071456477250, + 15037632622997844185, + 10281681147602922991, + 8387513215826982860, + 13397109138769038277, + 7084174620085887447, + 15381284784438265762, + 16976843333603073611, + 14274307629407002665, + 12473334862833791357, + 8997956760382491526, + 8298892662631420503, + 5472561286154586436, + 8315605310276598271, + 12474462379154230650, + 10445588651118201711, + 12749363600252668826, + 9674380161263743880, + 1900882316715526315, + 883896405076194513, + 1552264781530261426, + 16555531252289933360, + 16224734434535599431, + 15007188171410716378, + 11716803237395249254, + 12840697874030383079, + 13890029316710373383, + 1782726623768308002 + ], + { + "siblings": [ + "7100707161494325159815210527633100343831037416617119295335390238641062364110", + "18615011224400563618259710317333610359295860295390325971674174457350336861278", + "18638252510268202996223298810369156790614480636315660067869890882409247515443", + "3542557728292978470127328791878734439047118914032080805730763341033278400569", + "3383658525910102929816232820006431835958914486624572999178636193090882771374", + "11703833380245801316891951891810412983657065159558919794116340707286898922842", + "18446360279626056247154427334196276640440495966682744701473288902470045434408", + "9697206150044606393124219748356810225854286859173587127234397827322558117686", + "20220261037279928385606400738268111069963996663975531804406735564618299059378", + "16221141131165797863541296248947896432021429638674226935491624338794007671419", + "19125853975043551165586319231980106619362027349722738990956901646792780373691", + "3043548185124639868217950761751397710884664697012253267586864641630542679096" + ] + } + ], + [ + [ + 1148247527744869258, + 14966829861387300681, + 6970801868466370666, + 17474959496906866020, + 10299845591412520440, + 11065138039192921534, + 14197683118007391853, + 390806564933537212, + 958112066461504248, + 16922212280697809421, + 5475435978660182214, + 7283745360734478546, + 14078327148811124466, + 9923240992878260150, + 5617833048371102588, + 2255391223907802786, + 1408818665121848201, + 1685992602513474373, + 15299063041480314858, + 1491497660537993072, + 5932096700389104991, + 15968665248493286420, + 4548414910649505443, + 4114159122206720000, + 13834570641410248600, + 11675585804870176982, + 8110164457340162239, + 12978162209255760240, + 7407184414350621938, + 16197459831879662213, + 11350557882957924988, + 14329624091803998553, + 9210714617940189602, + 12143829786455885737, + 9514038998073896335, + 15056996021539419734, + 502181540395213788, + 10345671434947186593, + 14110105225319968417, + 4950486947079820638, + 16648286884200625165, + 15037064727555675911, + 133060784364305431, + 11424814340666268510, + 12782626941691346848, + 11688037940239744042, + 6569987102105667285, + 11823994862245623905, + 16470383983168898327, + 14877083309863442058, + 4262877476401225179, + 2346423205974998473, + 9498673983224081158, + 2282672205000603505, + 3235243981524538111, + 59618709398385389, + 2448784379634925126, + 12946321040071299108, + 13269751038373093080, + 5933807190104737568, + 16501370241433168355, + 10574336702216441393, + 12389469285607173181, + 17331390705920623101, + 9066417539125521816, + 11652906031482851325, + 8011583986547520173, + 16078491772079398923, + 2246113980788462843, + 18322687452713155332, + 1500313571418413039, + 8440396782156574075, + 2305022127583588329, + 1880072926765663120, + 5073535559680430634, + 405359483669222064, + 7324483206341405466, + 5712059102963268617, + 8841370168061432585, + 13209158968128702968, + 9376212756314696284, + 2151170279694679555, + 15551658094118296910, + 4455949478644419141, + 7358869238067506773, + 13969569878596557386, + 2916135154777441040, + 13271999093992186951, + 6054020491477938999, + 2554998084590288682, + 11735828345615952520, + 14775497567149507810, + 9297341623119498339, + 9652450173568415717, + 18300203886904387509, + 4507156440914598205, + 18412690527334782312, + 9635628088374728231, + 16126985334664469207, + 11442589993769058043, + 4969840564468077530, + 18360639437863437469, + 17007896916999652912, + 10656720445954376545, + 8484306427982641678, + 1368710066130592317, + 6330462521063831543, + 1414658908554180114, + 5767867944424729823, + 10647665226923790000, + 13817156138732044594, + 6429953576618971035, + 6339596636984878624, + 8256544243315053385, + 4753473094738780993, + 10005389287357096055, + 9081143915806255775, + 15742681565839594820, + 14168023072007780706, + 3380828782644677880, + 15536932068495907085, + 16625850317708502351, + 17395113215547819090, + 2678056819247226769, + 6274947302359501748, + 620778105802441223, + 3466445220405060405, + 12266165289236422816, + 18417380108839621474, + 9893365346204465964, + 9248678199899191142, + 14318172522483236255, + 17428190688065047125, + 8588333453225223647, + 8081928975277311024, + 6727781187046718168 + ], + { + "siblings": [ + "6163348912643180949752129804488319812178570777007368266300377075621484682302", + "15561578346496568427369689779774592149089147002017271112121876922948533072911", + "11029989624461664711149576569172065120232610183587252878711232311165318525934", + "4232300499900001916380594778126542283040984508535441631785195962570459217049", + "7064851153651010775344316736070967510284057353494827664901988141521982433341", + "3424272720904732165745730674004595561019188543725050864813596346560125920465", + "6771665205242547725232154490190460458815471196256444759609876108334046906616", + "5757822220975878694257679000056574181626652853931635733303045919981743078807", + "16288665841723658285381435988100840660648631128647660014288006744017609874044", + "6165974979292748929155793521128493118628461579092642121219691383131737080158", + "15930266484069425368819324938527410123257710596438979564703870945946137619600", + "7257894287989741726898018391468579257278143447520572614790148794953962678126" + ] + } + ], + [ + [ + 11911380244787082454, + 9704917403813347480, + 16204906838303474268, + 11246034917293857915, + 8845046497660106007, + 10552083827922892666, + 4871503888810260689, + 16606022361011593742, + 2979354473382220085, + 15656477654269737883, + 9942498380431942149, + 1158950332076370992, + 7662295017358541914, + 9422103349206380506, + 5485974184778263865, + 14891895456298739601, + 11168461339226058655, + 5433039515642088136, + 10604570659833395943, + 8750013952458951398 + ], + { + "siblings": [ + "3951072288786530590051970650055862141769864672799154651228413516552648230426", + "12130786047386314152303017024260418027918161507196749013798108576721189712588", + "2920298191609311617137942290574571318746135353111536060959380727200542538294", + "10518910924078873283454476121255465608156425882817790444390725058607472843085", + "6553616435152717494841693877556875931857162123340028874969495806755759883104", + "5846429153350401089970076078979942018735290257981184621396501814951621546079", + "13561227897720062787569982228391751148290173025300517391805349603843468642713", + "17166054885952757884666585658374297117518892182118090378646298008997413076080", + "20619857352840892846520936380624494886091888274187119977624109618885340368051", + "12452815822261033808387307335023638080153532547886374420306745422183915956732", + "11852292517285168113766797844824928838841473571797817861637169091764565795078", + "3010989178516099462115410463496392901586061165351528846269736308115608555029" + ] + } + ], + [ + [ + 1812197438412905718, + 17531644563348924352, + 1698797797749137081, + 5428041145359425253, + 1844115553745819608, + 5875145649337354067, + 3636838736155968963, + 7456741504396099617, + 269767359737315635, + 10492287456143697805, + 10683413152363931165, + 5805103575304773588, + 5709327109967871661, + 12070623677192796241, + 5512731461965172689, + 6219423422336025581 + ], + { + "siblings": [ + "6230232477426324583826799446050728086974536029259161579546120730923882607912", + "2315426617776818938503388571729287181018055892748549067713125026381667526465", + "14364878012406928007415086964129963456588117935227803032650757333040978443786", + "15007346864641236537093840990612815729031377193938267132090398056852956736157", + "18343616543794654013317956850083024478576235971689900332026826296792846678133", + "10853090058967557790652531111671461892680525789830083216298203202507059915290", + "20175270372437164024916342368140414102839017895260796709953075852612265980694", + "15449592984609509405317854371699150377730053033129554524666214177614734634808", + "4776392557999648771703826978078067565641531361970238912596607126110748058578", + "11266061626401139685245177802809286068383016426380975192329118213444933402032", + "18731388638295487310907132248077942648213652268354597938077927039456888235077", + "16817625655466290314397387194618263215722980174110622675168370599761029642745" + ] + } + ] + ] + }, + "steps": [ + { + "evals": [ + [ + 16109642997795428478, + 7750718609525825820 + ], + [ + 4163429572516407494, + 14303548843812229945 + ], + [ + 2315653224282290996, + 9627071364931648553 + ], + [ + 788321999551840335, + 17429048506731721025 + ], + [ + 5083502431408826796, + 6002692696686708599 + ], + [ + 16113128984778447213, + 540241704732294284 + ], + [ + 8047121407646292837, + 18125657270041156282 + ], + [ + 9243950205559354511, + 3203803602992164351 + ], + [ + 846059654018361777, + 6466168750581713633 + ], + [ + 6121548462795120572, + 13651718416786531638 + ], + [ + 16141172830332761058, + 5540573103234237436 + ], + [ + 2190799817644018798, + 1817110998614372402 + ], + [ + 17244162413302215528, + 14395505773785127949 + ], + [ + 14550806416138055337, + 846715096386943184 + ], + [ + 96421451193066370, + 15512483751009227622 + ], + [ + 1942367755260643236, + 3152013514459864026 + ] + ], + "merkle_proof": { + "siblings": [ + "5452649857454552055326780781805022176276323684805632502737759759482380627387", + "17775351471514642530248569342088394550439950210540191025709152794736917611955", + "4562246822979686974131814069300528215782604434753729239211372552777387011017", + "13047958752080312289870309624110584998504835229134160759065602169555772782367", + "2970166391572015254503090732368085710417667693695855171996447378067592390879", + "9164332655608262361108306219427950713210820445798729632405540662924428824269", + "9252094875227491369815590710349625709460070182641443484826555644528596419243", + "6779393963841391086805845988138791265084682874730858237522939854351030999588" + ] + } + }, + { + "evals": [ + [ + 1748592419639995032, + 12649776339630677776 + ], + [ + 8533689022924618499, + 1285815947920805448 + ], + [ + 17418802260712837707, + 11597025469977866391 + ], + [ + 12175764592520176671, + 8736658307188323017 + ], + [ + 9307192847078177387, + 9254485987310288642 + ], + [ + 10725990548122658562, + 12015671217617171198 + ], + [ + 18156502231717413735, + 16024484160984166896 + ], + [ + 16015688730167916681, + 243747712769216171 + ], + [ + 8834918147192444027, + 10627272483461649807 + ], + [ + 17401320133187367900, + 13732052199939618884 + ], + [ + 7433933528493604137, + 1474641608628534791 + ], + [ + 7920729153152625614, + 16566331916602985259 + ], + [ + 1225531494144838375, + 7384597392819504170 + ], + [ + 3670715566551088299, + 3331796132444466878 + ], + [ + 11875327252467275695, + 10874990073891265659 + ], + [ + 7506346039810665608, + 13443962453236822145 + ] + ], + "merkle_proof": { + "siblings": [ + "12076096784451690137260098161355814665408343278260315390761616275992944598821", + "6877138634499063303247372103641106402841647102984435585620725693331064466700", + "12322268526795276838854671388948135759299552472045654040047096794047101510661", + "21159502680001528868017408084643258408022894356504571319944071052653514862099" + ] + } + } + ] + }, + { + "initial_trees_proof": { + "evals_proofs": [ + [ + [ + 13796872146802299684, + 1192046352318644141, + 6787194230127606489, + 14021314722240481892, + 15053272126775250985, + 10336801592953102825, + 17910444972254474013, + 13826202445564261260, + 7511067966613177018, + 8533943460042554790, + 7594923189862840024, + 15140177399300239059, + 5322573689975815507, + 14639900213443911891, + 9497914493262954802, + 13827492102108388251, + 18339972884377028287, + 15298359122689140969, + 4484220907476506148, + 1694281816120798477, + 7972183306680911612, + 6894445851726306919, + 2602325030916449300, + 1425177176246867882, + 17002236095949555973, + 13444091540899518585, + 9036778905328112653, + 827134525551610073, + 16861037087036914375, + 13729085908255234261, + 17263846064333962014, + 16570013204373906958, + 3467597153271303057, + 18437362804524090884, + 8096667471204621073, + 5375327826406073445, + 15213345109211020514, + 1480621659774345574, + 8080713652611583477, + 16331484907562767348, + 2873086431531360683, + 11893537785332561382, + 9837579340705693187, + 7797530611224383870, + 11912642655833986533, + 8276729441993636083, + 9307425316361446087, + 8406529904949308357, + 10296065468143943246, + 17910303971531087604, + 1804108392456441397, + 17262978115306864034, + 7636859605304385219, + 4268755610754044755, + 5753438353712541466, + 17572427153578808221, + 12356318314585365790, + 4710880852823794394, + 16000195818681706954, + 6317485827816478374, + 10605179639958608310, + 9099889781705189800, + 6628047300187777374, + 9035109239839163280, + 17708254630353975064, + 1744158513652976041, + 6792208466743508272, + 9379568119742762348, + 15678621624683458855, + 15908741698115084675, + 11858394526463479297, + 2620404385382603907, + 8063967219295879382, + 10948100076679357821, + 11930303352867434359, + 7879081067980890234, + 13943025136480202826, + 18047808174852001750, + 6549064541738241245, + 13146454408733759153, + 15441736589289908259, + 15674453838039574310, + 11681903343226950814, + 14845163259669105418, + 17148681587101608621, + 14225993952131931553 + ], + { + "siblings": [ + "4185460081987594009859653396679189385240106617834479057730633259436560360282", + "2708209180559584291554612578622563407629237012109926337996257998563892095331", + "14719338068677845080225484109575240920980428568417451679759348697972883655100", + "5117536903536987218826963736251151406782903372648509964704356054819092976107", + "3433225581369434457489365164716474146617140099956860771366075226143136418257", + "11830704376945227715316994298361071166272306784888966260900636106157418305383", + "17298638778734519738188192277059406041990380655118898672220067557519119260770", + "4751510821913722972602946640345111089143604944353650765267836190139896796245", + "17777628662786967122849179509378368894693091903715643590429413493218841534852", + "12253341994499697425442578449379665136620636627029142272831755682677743040182", + "14811880887860353654218435745951777701481179795239623636876672792487507099152", + "8686560674071151533677187513287259883834482440129541300993699268553829607764" + ] + } + ], + [ + [ + 13160480101978903874, + 10759677247734278685, + 6083420057072134812, + 1587779352728539290, + 4676615036999971791, + 16465261227639316134, + 8936192909548946610, + 15654103443400911273, + 4376651520135913071, + 6395722382224180048, + 13915113149898387434, + 17288008310833493486, + 3850725702088802331, + 12590635248736107909, + 7154242396647472480, + 4857024832336341484, + 10532943266568481950, + 7949524058850522015, + 16651360009036322718, + 15939263751095989689, + 15545253417388873212, + 2854907726317946786, + 13352513928889290664, + 17472124860440643311, + 4481168552244103243, + 12740692192871317806, + 8619073303996950849, + 15936930856800622765, + 5049110277693395261, + 1117841376538789472, + 8239769722301698904, + 7059505362051430435, + 746382161738860048, + 5661048243063814600, + 2884786473137270040, + 16013604605574539841, + 17704670359922098031, + 2173811981545450361, + 2953368793732066052, + 542346176484520350, + 14591324673460614485, + 8890795039084574340, + 2144041414869796536, + 16815847253986110643, + 9080037507529499865, + 7272069679733244476, + 4891144041266007661, + 15644217494348922897, + 9620072203282670253, + 8466111847494961373, + 12485951233213825551, + 5876414857620807250, + 10155907566084345808, + 7250047464792898425, + 7065640892330765190, + 13939240669235540460, + 16626556840014741214, + 8651663631204475930, + 18302243783466619298, + 15994811948266311181, + 6444565906319135679, + 4354362769794519793, + 982163547476236634, + 11681477570764226085, + 7045432289561409786, + 785486593561859082, + 2051107398781902561, + 2852699119552556466, + 14652589974397740226, + 3713034579296211470, + 7956823820351306248, + 15759478724189244365, + 2211608157338041907, + 11693820538035762472, + 15100273991075147280, + 10088724179440089493, + 14612367743098949116, + 12913802052931475408, + 1387976311104076878, + 2675647010694385571, + 16833740123875086084, + 15701307681354816519, + 2993988329677998715, + 17559824380271099719, + 15215059522652394901, + 6149052109934895553, + 15098826265531224940, + 10703975571647325591, + 14370611294222499804, + 12620770882284601359, + 11457381284964538606, + 11221104755201354825, + 16357087367308046914, + 5868882906674403768, + 4748910172475538175, + 8688119265331889800, + 3379119935068277904, + 17349170695486104094, + 4505159502398075783, + 8810972444564218019, + 123365961420307341, + 8162790987965822796, + 10643321142494476717, + 8715764916926059136, + 2501247987309239415, + 14155587068756647672, + 14217620960544994261, + 3834298921069906846, + 12150184609094080389, + 14402211836027820257, + 17679454346820345557, + 16088046943166404874, + 13846358411454235145, + 12970577319030396765, + 4335267947019058492, + 13481679457414925621, + 11419004787157647790, + 14317532998905527516, + 958422329151781602, + 9801932902962493052, + 17794081506632657753, + 18438951031140838349, + 18434587297621757222, + 2139542909697496766, + 17441145181210383085, + 15204197028091520418, + 17298435066732867185, + 6715575222504021159, + 726637067392635216, + 5653087015714265973, + 11751140092920544981, + 14603954302283312059, + 18382383336236221662, + 535858311246719749, + 6735668968955212700, + 15605929246583689016 + ], + { + "siblings": [ + "8276768421367167813084018675307238617331446769903801769202876719101315395531", + "3979178457616110302642811766921915191963898395218971335589045651199915025355", + "10483152279252869000518256939528319060727495380364071244826727995502432072484", + "6215282649373040910642637874240172969814166204927428722367450563159774292381", + "3271403885975057376419228028790889444148216606338149146341530391006301895744", + "8771893362735829955134188883123710527151591118584420614265474033858468693291", + "1344808883638639366084977129961153442584383743052648614458454362613935140792", + "11198790865314961254103768268366973722380081503020891950993149011653099281926", + "1555968025961091224163037528577677081579284079181334058990166496211136354210", + "8359030393360912356117320004654543222004865043628199090418252353289224510127", + "11424417914029262018202470717296182601282680600987289645690418658652670180065", + "3178153116491368583443915659041559605596799612324563983697841454174110307012" + ] + } + ], + [ + [ + 2075810974022119068, + 6240368653458325476, + 11644795226307082124, + 4741471250119429948, + 12953738956266456659, + 14172784622403914379, + 15882016292388549187, + 3681112190729528597, + 9708858309556792516, + 14088023252444896592, + 8114864086363896121, + 11083307841760736885, + 7491909536982374757, + 6939617542935232512, + 5457802368609145997, + 5666187451786872644, + 6615033462010253647, + 17063374177035096757, + 13930158855289564871, + 5551211886206093368 + ], + { + "siblings": [ + "17347256274469147158943196844346661986311915200478375252628062092774030623480", + "5744728924336585274260422873204770569352373423587331843238651403245835119524", + "7876322447035570975981991841349475349555055059404368172046732293224341131850", + "3860610591055432475774405603214236656794329141989884821723505263356111797753", + "4049886239143047712742071246964167580600858484707723117890513276635616024899", + "11642712146689656810432794670227333698754288093776811867250633270938616925025", + "5495743961830038218363924241912500593668607171619042870528836628283740871627", + "11763609266128546220862219036472754046375349035398310451618462354808354898669", + "19748831216282168937804484279520132439212088679031874876979687328363804916042", + "1157011882052646477973679994518060115928817156512638141758436686045461417853", + "3472831697531025567708094386593135385418323012098049142163571431898640838286", + "10214114189982184880740341212695611376511442828222541722127539126741674103122" + ] + } + ], + [ + [ + 4057011427396074007, + 10281325853322362658, + 16970332267472420849, + 5047621431653331284, + 2889786145478235324, + 1298697772227610802, + 17147851157561063659, + 13065912338054315807, + 372080041549607810, + 4473554825329786746, + 14265357157251183001, + 7131489049816247456, + 10119070829351748135, + 3593178261489190875, + 9177905250571870947, + 16767213671965416644 + ], + { + "siblings": [ + "21789562915182992237810559261422169213801233513441765528252875667787024299016", + "17586726068706199236591552458494641593810734136396878904064599387611335271257", + "8463071341598892615449969288706785010763188158615005211404651324827937520335", + "13605775118683812219133161175007549039507127670696491959170320598938262976415", + "8498376004658435759906705356597200825623783036030831959148274492523213620740", + "11660467539170059831447676678163755848748653530111293838956198777245515545761", + "10329422025833839282456555090612440737728843429346812915769421581013412903809", + "6498433859695860570233707858894236600547217486205955052270578915144214905342", + "3643687003532448306689061837042552013473303452022768355871989082579555539734", + "15230119237490875026476648984612583353987586904639266214357566186472141964124", + "9710397341342042284522320390343141056904888036876005007697405380081256837647", + "8282824731644233838946413470784485467279767367920565649473764230825848386981" + ] + } + ] + ] + }, + "steps": [ + { + "evals": [ + [ + 2115386950524490659, + 1027382456623070343 + ], + [ + 12524633107608046610, + 4943339150892733485 + ], + [ + 7745299546380425954, + 11939538173321127449 + ], + [ + 1200448643956079801, + 12979013934647478212 + ], + [ + 4939415874313549811, + 7101470357882302365 + ], + [ + 223620929672930999, + 12555180981415421973 + ], + [ + 14891882392818363872, + 4438989719559331090 + ], + [ + 11567444039321700824, + 4564261707378273701 + ], + [ + 4982403251118485585, + 8206386745070895116 + ], + [ + 11250239258369155483, + 2465197716090261812 + ], + [ + 14836659859433257191, + 5327198479143342591 + ], + [ + 11222841699995600875, + 17626844735568794961 + ], + [ + 16540712308155225401, + 8917251449332707080 + ], + [ + 10739412040901037984, + 3128497476900934176 + ], + [ + 14040266161634561648, + 15662389070403882688 + ], + [ + 15748092009379937125, + 14256059699691155089 + ] + ], + "merkle_proof": { + "siblings": [ + "7915263023645944495965252121534347678673183670377173471367172971211132237267", + "1269664418597635726779334459022264272689503362348056177438579312987679537410", + "6445869752418071701794484855153789503703640096326581206417713088859637768434", + "16924389154225255221402432377246460724442499884192909010683907235523039810665", + "12089185211947104289556977595249904641788102476437842325308933036837695661602", + "3448246430116586160161475482777304026775194449710651471444684711180369071941", + "5279765742302665737163033721351324659145179138570986487909161353876751148789", + "560978010046223082094140079151396233410143894605210839869980714884980384674" + ] + } + }, + { + "evals": [ + [ + 1692072549307634329, + 9456462947852052766 + ], + [ + 4345553979469606588, + 6151435927065690022 + ], + [ + 4274948691979734157, + 10048532955737081446 + ], + [ + 3674589836231520717, + 6172690912560841817 + ], + [ + 3693505440122684594, + 13602697785914968207 + ], + [ + 17455950386086779267, + 13696495348346182768 + ], + [ + 55878182725749325, + 254961530138030090 + ], + [ + 2705612763342660187, + 219620753011672979 + ], + [ + 9911944505845127126, + 16722823764501159254 + ], + [ + 16668370857955283584, + 11836587322856905899 + ], + [ + 4489220730861810674, + 7069354018791568636 + ], + [ + 1367487434129765348, + 5211758472424783817 + ], + [ + 8026970967932726418, + 15171212002206349395 + ], + [ + 15330064702880151303, + 12864636764552903143 + ], + [ + 3615644251012278590, + 18431988495282132544 + ], + [ + 9425793191482054047, + 1828307231887800204 + ] + ], + "merkle_proof": { + "siblings": [ + "1779077242447952901052715405912208576959329561861225084097613082951992030585", + "16404750671527415170078512043953793871592898428335897797769637292879470134634", + "9837237760131412192955546734659152136254038228743904218645601553339315129693", + "20673382058346043337645852373656534189599352693149688645395368743089387881615" + ] + } + } + ] + } + ], + "final_poly": { + "coeffs": [ + [ + 10321582036114144171, + 4110557890612205914 + ], + [ + 17281315714250494540, + 5905427443022680477 + ], + [ + 4816427921052889757, + 11590366991627667939 + ], + [ + 8593698307390547161, + 17798002042082854267 + ], + [ + 16708372292656791930, + 13292520348780552479 + ], + [ + 1188416792570434107, + 6532376959656381049 + ], + [ + 14886584914481523311, + 14559003499970896000 + ], + [ + 11677301406268795190, + 11298561049328627998 + ], + [ + 259342954131535207, + 552334986737946894 + ], + [ + 7161985668866845208, + 4407421329765055267 + ], + [ + 13894332537441191829, + 3715950693159097722 + ], + [ + 15028103092488925871, + 9776443862422000054 + ], + [ + 1100914231103829823, + 3609362746290196936 + ], + [ + 10266149616871580883, + 5334000564649443219 + ], + [ + 16797599121072108435, + 12520468173491687686 + ], + [ + 13228694136367945719, + 6945139589197346626 + ], + [ + 4382282866448161191, + 12928761286154072667 + ], + [ + 4434917028912527815, + 5341839113290415433 + ], + [ + 3584147290048792319, + 7842901653228622970 + ], + [ + 2051981906040326592, + 1708342571175917735 + ], + [ + 1486994408242908976, + 12142370507916330347 + ], + [ + 14572423428165558316, + 4515760458714018335 + ], + [ + 688400868891522195, + 17315503532264710647 + ], + [ + 2505817476995641748, + 15694365057899201297 + ], + [ + 13697535208283597488, + 11879647749358465161 + ], + [ + 4956300689924480800, + 2804735771711363051 + ], + [ + 11252831917996122965, + 5478830316339895373 + ], + [ + 16664212911012212286, + 7790742766328214411 + ], + [ + 7523981210275590019, + 9250658585866801361 + ], + [ + 15370510976458911835, + 5850568843187876841 + ], + [ + 11837697340087872042, + 16297385663967034244 + ], + [ + 13874675370883697825, + 18090826027484145362 + ] + ] + }, + "pow_witness": 8070450530368882813 + } + }, + "public_inputs": [ + 47, + 101, + 102, + 199, + 65, + 30, + 223, + 235, + 160, + 78, + 188, + 214, + 140, + 94, + 205, + 188, + 142, + 149, + 191, + 101, + 218, + 71, + 239, + 85, + 61, + 109, + 133, + 55, + 32, + 11, + 116, + 250, + 530507, + 12, + 7, + 108, + 35, + 28, + 90, + 62, + 21, + 176, + 50, + 136, + 186, + 251, + 254, + 16, + 238, + 134, + 189, + 10, + 210, + 63, + 159, + 236, + 200, + 110, + 224, + 63, + 180, + 57, + 224, + 69, + 246, + 496, + 243, + 56, + 163, + 79, + 50, + 190, + 245, + 166, + 174, + 154, + 24, + 226, + 216, + 77, + 87, + 86, + 137, + 243, + 105, + 31, + 72, + 212, + 237, + 21, + 87, + 167, + 90, + 84, + 73, + 174, + 7, + 149, + 160, + 195, + 98, + 125, + 232, + 107, + 227, + 232, + 132, + 63, + 195, + 108, + 80, + 142, + 140, + 117, + 128, + 169, + 147, + 164, + 22, + 189, + 175, + 40, + 167, + 182, + 95, + 91, + 115, + 64, + 97, + 205, + 102, + 20, + 109, + 108, + 3, + 105, + 214, + 125, + 138, + 237, + 126, + 36, + 31, + 19, + 215, + 199, + 234, + 135, + 59, + 195, + 161, + 143, + 126, + 141, + 218, + 96, + 213, + 61, + 141, + 209, + 152, + 88, + 217, + 7, + 47, + 245, + 220, + 231, + 181, + 242, + 142, + 53, + 47, + 24, + 201, + 184, + 151, + 2, + 38, + 179, + 163, + 236, + 149, + 226, + 89, + 13, + 11, + 159, + 217, + 95, + 187, + 192, + 163, + 74, + 245, + 217, + 189, + 6, + 186, + 209, + 230, + 94, + 10, + 158, + 123, + 1, + 199, + 242, + 177, + 38, + 224, + 42, + 2, + 2, + 60, + 205, + 29, + 196, + 59, + 220, + 108, + 112, + 55, + 104, + 250, + 157, + 27, + 20, + 130, + 179, + 179, + 215, + 236, + 80, + 209, + 20, + 182, + 157, + 178, + 242, + 234, + 164, + 9, + 114, + 14, + 36, + 46, + 74, + 115, + 50, + 107, + 154, + 22, + 141, + 127, + 138, + 218, + 51, + 60, + 146, + 140, + 142, + 177, + 188, + 232, + 133, + 59, + 89, + 93, + 132, + 150, + 12, + 32, + 181, + 45, + 108, + 95, + 68, + 141, + 240, + 88, + 235, + 7, + 34, + 140, + 87, + 19, + 161, + 104, + 88, + 172, + 82, + 36, + 139, + 7, + 136, + 9, + 144, + 115, + 100, + 13, + 195, + 95, + 251, + 128, + 208, + 165, + 135, + 171, + 195, + 43, + 27, + 161, + 61, + 190, + 250, + 69, + 226, + 131, + 18, + 8, + 212, + 22, + 124, + 147, + 11, + 114, + 93, + 208, + 203, + 29, + 14, + 132, + 196, + 95, + 91, + 11, + 62, + 190, + 60, + 19, + 174, + 19, + 57, + 218, + 71, + 204, + 106, + 45, + 89, + 103, + 12, + 68, + 97, + 131, + 59, + 104, + 173, + 177, + 22, + 187, + 222, + 196, + 64, + 18, + 168, + 115, + 65, + 165, + 4, + 55, + 75, + 151, + 134, + 231, + 5, + 202, + 220, + 69, + 106, + 172, + 36, + 61, + 152, + 68, + 185, + 231, + 113, + 132, + 139, + 184, + 243, + 86, + 175, + 149, + 8, + 70, + 157, + 185, + 218, + 236, + 106, + 139, + 91, + 214, + 24, + 153, + 153, + 239, + 5, + 12, + 7, + 25, + 39, + 229, + 2, + 11, + 192, + 150, + 83, + 1, + 193, + 162, + 160, + 151, + 164, + 242, + 98, + 88, + 56, + 230, + 0, + 121, + 168, + 19, + 26, + 175, + 24, + 151, + 242, + 171, + 68, + 159, + 6, + 163, + 218, + 21, + 28, + 186, + 199, + 45, + 237, + 152, + 87, + 134, + 249, + 150, + 235, + 182, + 215, + 167, + 67, + 194, + 200, + 55, + 35, + 206, + 169, + 241, + 120, + 3, + 153, + 221, + 210, + 158, + 190, + 70, + 172, + 10, + 190, + 167, + 189, + 118, + 161, + 153, + 107, + 56, + 83, + 51, + 48, + 105, + 244, + 55, + 69, + 99, + 127, + 3, + 63, + 21, + 33, + 30, + 110, + 29, + 241, + 71, + 84, + 197, + 40, + 92, + 173, + 95, + 214, + 2, + 6, + 236, + 202, + 62, + 80, + 249, + 89, + 237, + 35, + 36, + 250, + 231, + 8, + 128, + 83, + 4, + 171, + 182, + 163, + 244, + 187, + 57, + 211, + 5, + 208, + 20, + 142, + 153, + 254, + 1, + 167, + 137, + 143, + 249, + 89, + 235, + 80, + 61, + 247, + 150, + 91, + 17, + 242, + 24, + 15, + 81, + 218, + 234, + 47, + 112, + 129, + 87, + 216, + 56, + 163, + 96, + 169, + 31, + 30, + 212, + 142, + 109, + 126, + 162, + 195, + 174, + 91, + 220, + 75, + 121, + 40, + 138, + 106, + 236, + 24, + 62, + 179, + 80, + 20, + 230, + 214, + 33, + 240, + 64, + 72, + 172, + 153, + 9, + 186, + 166, + 23, + 4, + 73, + 175, + 43, + 123, + 236, + 134, + 111, + 101, + 141, + 87, + 199, + 201, + 131, + 148, + 138, + 207, + 119, + 139, + 143, + 56, + 79, + 95, + 152, + 229, + 51, + 13, + 61, + 192, + 72, + 65, + 11, + 140, + 142, + 165, + 1, + 222, + 30, + 132, + 128, + 77, + 246, + 121, + 54, + 200, + 248, + 234, + 145, + 206, + 173, + 141, + 173, + 228, + 76, + 86, + 72, + 74, + 236, + 195, + 211, + 88, + 119, + 228, + 113, + 83, + 40, + 246, + 233, + 151, + 220, + 11, + 155, + 214, + 14, + 201, + 215, + 153, + 12, + 152, + 229, + 33, + 95, + 229, + 230, + 155, + 61, + 111, + 128, + 139, + 247, + 5, + 21, + 150, + 52, + 152, + 86, + 146, + 170, + 110, + 85, + 174, + 77, + 8, + 95, + 166, + 134, + 2, + 158, + 161, + 155, + 29, + 139, + 181, + 79, + 199, + 203, + 252, + 170, + 237, + 150, + 234, + 208, + 100, + 59, + 136, + 213, + 70, + 16, + 113, + 171, + 80, + 33, + 120, + 97, + 85, + 96, + 203, + 238, + 143, + 243, + 103, + 165, + 241, + 196, + 212, + 77, + 80, + 43, + 112, + 12, + 108, + 78, + 177, + 89, + 129, + 62, + 95, + 73, + 64, + 31, + 125, + 152, + 116, + 234, + 100, + 189, + 149, + 143, + 13, + 72, + 12, + 27, + 45, + 15, + 178, + 77, + 1, + 83, + 191, + 221, + 37, + 193, + 185, + 19, + 44, + 33, + 195, + 102, + 107, + 43, + 113, + 202, + 211, + 77, + 49, + 74, + 84, + 39, + 173, + 5, + 52, + 53, + 138, + 206, + 27, + 124, + 112, + 50, + 30, + 125, + 114, + 161, + 101, + 249, + 103, + 120, + 195, + 71, + 99, + 221, + 176, + 7, + 162, + 229, + 244, + 42, + 25, + 159, + 96, + 93, + 152, + 63, + 117, + 180, + 94, + 203, + 243, + 68, + 15, + 184, + 112, + 21, + 171, + 17, + 121, + 117, + 219, + 84, + 146, + 63, + 1, + 118, + 93, + 60, + 109, + 198, + 180, + 113, + 139, + 53, + 73, + 60, + 248, + 96, + 170, + 216, + 36, + 181, + 61, + 180, + 184, + 197, + 36, + 176, + 163, + 203, + 15, + 236, + 255, + 99, + 31, + 42, + 237, + 196, + 189, + 136, + 65, + 19, + 4, + 189, + 77, + 155, + 8, + 139, + 201, + 3, + 46, + 69, + 89, + 223, + 52, + 166, + 176, + 235, + 188, + 12, + 237, + 32, + 90, + 140, + 57, + 122, + 222, + 4, + 228, + 87, + 43, + 218, + 215, + 132, + 189, + 17, + 151, + 85, + 185, + 130, + 216, + 30, + 78, + 153, + 184, + 170, + 122, + 220, + 135, + 248, + 165, + 196, + 18, + 198, + 180, + 192, + 252, + 17, + 77, + 46, + 2, + 237, + 237, + 160, + 129, + 140, + 242, + 49, + 108, + 97, + 65, + 119, + 200, + 121, + 53, + 155, + 146, + 190, + 124, + 118, + 57, + 209, + 227, + 73, + 37, + 43, + 51, + 12, + 44, + 99, + 156, + 57, + 106, + 217, + 192, + 32, + 39, + 112, + 209, + 56, + 169, + 156, + 39, + 247, + 33, + 251, + 5, + 124, + 121, + 160, + 77, + 80, + 40, + 206, + 227, + 75, + 176, + 207, + 69, + 182, + 121, + 121, + 223, + 115, + 114, + 102, + 22, + 168, + 204, + 22, + 24, + 48, + 49, + 162, + 219, + 75, + 146, + 88, + 180, + 41, + 184, + 209, + 73, + 28, + 7, + 42, + 33, + 77, + 35, + 192, + 56, + 240, + 99, + 224, + 239, + 31, + 238, + 52, + 20, + 174, + 185, + 187, + 93, + 2, + 16, + 240, + 117, + 238, + 57, + 73, + 91, + 113, + 39, + 222, + 160, + 167, + 84, + 75, + 106, + 43, + 229, + 239, + 178, + 232, + 185, + 141, + 13, + 10, + 102, + 51, + 53, + 79, + 149, + 50, + 253, + 131, + 161, + 2, + 49, + 128, + 22, + 196, + 164, + 88, + 29, + 53, + 123, + 203, + 140, + 252, + 0, + 255, + 231, + 108, + 155, + 64, + 36, + 21, + 115, + 125, + 211, + 51, + 133, + 61, + 50, + 26, + 171, + 195, + 12, + 101, + 45, + 237, + 75, + 253, + 87, + 84, + 164, + 93, + 174, + 243, + 112, + 128, + 213, + 222, + 23, + 87, + 55, + 71, + 62, + 32, + 155, + 194, + 103, + 114, + 235, + 200, + 20, + 133, + 239, + 120, + 146, + 146, + 106, + 154, + 146, + 4, + 82, + 246, + 154, + 146, + 68, + 111, + 2, + 88, + 170, + 132, + 7, + 161, + 112, + 251, + 109, + 113, + 91, + 65, + 23, + 63, + 118, + 54, + 156, + 247, + 161, + 140, + 97, + 99, + 176, + 176, + 189, + 59, + 52, + 110, + 147, + 233, + 78, + 28, + 131, + 149, + 185, + 163, + 251, + 179, + 199, + 45, + 58, + 22, + 45, + 232, + 3, + 112, + 154, + 43, + 73, + 128, + 47, + 236, + 111, + 128, + 50, + 113, + 125, + 88, + 216, + 106, + 78, + 15, + 223, + 129, + 208, + 221, + 82, + 33, + 23, + 7, + 114, + 152, + 215, + 15, + 89, + 196, + 120, + 191, + 146, + 61, + 43, + 28, + 242, + 215, + 27, + 174, + 144, + 5, + 96, + 238, + 56, + 116, + 214, + 247, + 155, + 165, + 75, + 180, + 249, + 182, + 41, + 114, + 233, + 5, + 160, + 204, + 66, + 136, + 228, + 66, + 135, + 151, + 23, + 189, + 98, + 3, + 95, + 204, + 244, + 137, + 190, + 164, + 124, + 198, + 148, + 159, + 37, + 236, + 27, + 38, + 47, + 14, + 45, + 255, + 92, + 44, + 150, + 159, + 222, + 131, + 77, + 242, + 223, + 82, + 2, + 83, + 60, + 239, + 59, + 240, + 100, + 159, + 98, + 241, + 170, + 246, + 41, + 123, + 134, + 179, + 116, + 148, + 72, + 214, + 108, + 196, + 61, + 234, + 218, + 73, + 148, + 12, + 57, + 18, + 164, + 236, + 73, + 22, + 52, + 64, + 88, + 232, + 240, + 101, + 17122441374070351185, + 18368451173317844989, + 5752543660850962321, + 1428786498560175815 + ] +} diff --git a/verifier/data/step/verifier_only_circuit_data.json b/verifier/data/step/verifier_only_circuit_data.json new file mode 100644 index 0000000..f68cc92 --- /dev/null +++ b/verifier/data/step/verifier_only_circuit_data.json @@ -0,0 +1,21 @@ +{ + "constants_sigmas_cap": [ + "16410135397206963995867986152754239948699603273283903389293816335827918317917", + "793737431233885020076403438726099627357557537710771017261200370525509120433", + "12956281394520952097582330637773878261111274369940411254759688417761804822142", + "10577530380775003887407451820221412218265659263471194993014549768898454599785", + "13610846379681807478607563401071620391800469867382019709290833315244210704863", + "765151448660164966011013501838259753360401123903311092227424737087007538841", + "13786717651422653112944870403443265466526140408716569251322854236333823743208", + "12716088402533018234480445545939519356897157402541455414075663659898205294136", + "7714394992134137076670975536966103814585482420260383440808539140364081464561", + "21494844788603743891376885362562637287120172946709821128154824772001032728080", + "14153637094178605853060659242981358456456672896438884686797867119060652807634", + "8426523842338951741294543051254253278084158527312126154422449980067255373785", + "9336152063716553400528035177375603771317196761317425271006398060378250593421", + "19032686473689874529303788521545715886983137707759075261782048632012085567581", + "15713676428971866339564327334872368460630508652571308740737040859682008007854", + "11466448479127530610447443676955276964009242931295623425740153710621884444011" + ], + "circuit_digest": "9787759494185596126611266365248694578977961103378519017707766709237231108177" +} diff --git a/verifier/internal/plonk/plonk_test.go b/verifier/internal/plonk/plonk_test.go index b2d86f8..92ff1b1 100644 --- a/verifier/internal/plonk/plonk_test.go +++ b/verifier/internal/plonk/plonk_test.go @@ -24,7 +24,7 @@ func (circuit *TestPlonkCircuit) Define(api frontend.API) error { verifierChip := verifier.NewVerifierChip(api, commonCircuitData) publicInputsHash := verifierChip.GetPublicInputsHash(proofWithPis.PublicInputs) - proofChallenges := verifierChip.GetChallenges(proofWithPis, publicInputsHash, commonCircuitData, verifierOnlyCircuitData) + proofChallenges := verifierChip.GetChallenges(proofWithPis.Proof, publicInputsHash, commonCircuitData, verifierOnlyCircuitData) fieldAPI := field.NewFieldAPI(api) qeAPI := field.NewQuadraticExtensionAPI(api, fieldAPI) diff --git a/verifier/verifier.go b/verifier/verifier.go index 02d66ae..16dd985 100644 --- a/verifier/verifier.go +++ b/verifier/verifier.go @@ -47,7 +47,7 @@ func (c *VerifierChip) GetPublicInputsHash(publicInputs []field.F) poseidon.Pose } func (c *VerifierChip) GetChallenges( - proofWithPis common.ProofWithPublicInputs, + proof common.Proof, publicInputsHash poseidon.PoseidonHashOut, commonData common.CommonCircuitData, verifierData common.VerifierOnlyCircuitData, @@ -60,17 +60,17 @@ func (c *VerifierChip) GetChallenges( challenger.ObserveBN128Hash(circuitDigest) challenger.ObserveHash(publicInputsHash) - challenger.ObserveCap(proofWithPis.Proof.WiresCap) + challenger.ObserveCap(proof.WiresCap) plonkBetas := challenger.GetNChallenges(numChallenges) plonkGammas := challenger.GetNChallenges(numChallenges) - challenger.ObserveCap(proofWithPis.Proof.PlonkZsPartialProductsCap) + challenger.ObserveCap(proof.PlonkZsPartialProductsCap) plonkAlphas := challenger.GetNChallenges(numChallenges) - challenger.ObserveCap(proofWithPis.Proof.QuotientPolysCap) + challenger.ObserveCap(proof.QuotientPolysCap) plonkZeta := challenger.GetExtensionChallenge() - challenger.ObserveOpenings(fri.ToFriOpenings(proofWithPis.Proof.Openings)) + challenger.ObserveOpenings(fri.ToFriOpenings(proof.Openings)) return common.ProofChallenges{ PlonkBetas: plonkBetas, @@ -78,9 +78,9 @@ func (c *VerifierChip) GetChallenges( PlonkAlphas: plonkAlphas, PlonkZeta: plonkZeta, FriChallenges: challenger.GetFriChallenges( - proofWithPis.Proof.OpeningProof.CommitPhaseMerkleCaps, - proofWithPis.Proof.OpeningProof.FinalPoly, - proofWithPis.Proof.OpeningProof.PowWitness, + proof.OpeningProof.CommitPhaseMerkleCaps, + proof.OpeningProof.FinalPoly, + proof.OpeningProof.PowWitness, commonData.DegreeBits, config.FriConfig, ), @@ -154,18 +154,20 @@ func (c *VerifierChip) generateProofInput(commonData common.CommonCircuitData) c } */ -func (c *VerifierChip) Verify(proofWithPis common.ProofWithPublicInputs, verifierData common.VerifierOnlyCircuitData, commonData common.CommonCircuitData) { +func (c *VerifierChip) Verify(proof common.Proof, publicInputs []field.F, verifierData common.VerifierOnlyCircuitData, commonData common.CommonCircuitData) { + // TODO: Need to range check all the proof and public input elements to make sure they are within goldilocks field + // Generate the parts of the witness that is for the plonky2 proof input - publicInputsHash := c.GetPublicInputsHash(proofWithPis.PublicInputs) - proofChallenges := c.GetChallenges(proofWithPis, publicInputsHash, commonData, verifierData) + publicInputsHash := c.GetPublicInputsHash(publicInputs) + proofChallenges := c.GetChallenges(proof, publicInputsHash, commonData, verifierData) - c.plonkChip.Verify(proofChallenges, proofWithPis.Proof.Openings, publicInputsHash) + c.plonkChip.Verify(proofChallenges, proof.Openings, publicInputsHash) initialMerkleCaps := []common.MerkleCap{ verifierData.ConstantSigmasCap, - proofWithPis.Proof.WiresCap, - proofWithPis.Proof.PlonkZsPartialProductsCap, - proofWithPis.Proof.QuotientPolysCap, + proof.WiresCap, + proof.PlonkZsPartialProductsCap, + proof.QuotientPolysCap, } // Seems like there is a bug in the emulated field code. @@ -189,9 +191,9 @@ func (c *VerifierChip) Verify(proofWithPis common.ProofWithPublicInputs, verifie c.friChip.VerifyFriProof( fri.GetFriInstance(&commonData, c.qeAPI, proofChallenges.PlonkZeta, commonData.DegreeBits), - fri.ToFriOpenings(proofWithPis.Proof.Openings), + fri.ToFriOpenings(proof.Openings), &proofChallenges.FriChallenges, initialMerkleCaps, - &proofWithPis.Proof.OpeningProof, + &proof.OpeningProof, ) } diff --git a/verifier/verifier_test.go b/verifier/verifier_test.go index 7d1d576..a98cadd 100644 --- a/verifier/verifier_test.go +++ b/verifier/verifier_test.go @@ -3,42 +3,121 @@ package verifier_test import ( "testing" + "github.com/consensys/gnark-crypto/ecc" + "github.com/consensys/gnark/backend" "github.com/consensys/gnark/frontend" + "github.com/consensys/gnark/std/math/emulated" "github.com/consensys/gnark/test" "github.com/succinctlabs/gnark-plonky2-verifier/field" "github.com/succinctlabs/gnark-plonky2-verifier/verifier" + "github.com/succinctlabs/gnark-plonky2-verifier/verifier/common" "github.com/succinctlabs/gnark-plonky2-verifier/verifier/utils" ) type TestVerifierCircuit struct { - proofWithPIsFilename string `gnark:"-"` - commonCircuitDataFilename string `gnark:"-"` - verifierOnlyCircuitDataFilename string `gnark:"-"` + Proof common.Proof + PublicInputs []field.F `gnark:",public"` + + verifierChip *verifier.VerifierChip `gnark:"-"` + plonky2CircuitName string `gnark:"-"` } func (c *TestVerifierCircuit) Define(api frontend.API) error { - proofWithPis := utils.DeserializeProofWithPublicInputs(c.proofWithPIsFilename) - commonCircuitData := utils.DeserializeCommonCircuitData(c.commonCircuitDataFilename) - verfierOnlyCircuitData := utils.DeserializeVerifierOnlyCircuitData(c.verifierOnlyCircuitDataFilename) + circuitDirname := "./data/" + c.plonky2CircuitName + "/" + commonCircuitData := utils.DeserializeCommonCircuitData(circuitDirname + "common_circuit_data.json") + verifierOnlyCircuitData := utils.DeserializeVerifierOnlyCircuitData(circuitDirname + "verifier_only_circuit_data.json") + + c.verifierChip = verifier.NewVerifierChip(api, commonCircuitData) + + c.verifierChip.Verify(c.Proof, c.PublicInputs, verifierOnlyCircuitData, commonCircuitData) - verifierChip := verifier.NewVerifierChip(api, commonCircuitData) - verifierChip.Verify(proofWithPis, verfierOnlyCircuitData, commonCircuitData) return nil } -func TestDecodeBlockVerifier(t *testing.T) { +func TestStepVerifier(t *testing.T) { assert := test.NewAssert(t) testCase := func() { + plonky2Circuit := "step" + proofWithPis := utils.DeserializeProofWithPublicInputs("./data/" + plonky2Circuit + "/proof_with_public_inputs.json") circuit := TestVerifierCircuit{ - proofWithPIsFilename: "./data/decode_block/proof_with_public_inputs.json", - commonCircuitDataFilename: "./data/decode_block/common_circuit_data.json", - verifierOnlyCircuitDataFilename: "./data/decode_block/verifier_only_circuit_data.json", + plonky2CircuitName: plonky2Circuit, + Proof: proofWithPis.Proof, + PublicInputs: proofWithPis.PublicInputs, + } + + proofWithPis2 := utils.DeserializeProofWithPublicInputs("./data/" + plonky2Circuit + "/proof_with_public_inputs.json") + witness := TestVerifierCircuit{ + plonky2CircuitName: plonky2Circuit, + Proof: proofWithPis2.Proof, + PublicInputs: proofWithPis2.PublicInputs, } - witness := TestVerifierCircuit{} err := test.IsSolved(&circuit, &witness, field.TEST_CURVE.ScalarField()) assert.NoError(err) } testCase() } + +func TestStepVerifier2(t *testing.T) { + assert := test.NewAssert(t) + + plonky2Circuit := "step" + proofWithPis := utils.DeserializeProofWithPublicInputs("./data/" + plonky2Circuit + "/proof_with_public_inputs.json") + circuit := TestVerifierCircuit{ + plonky2CircuitName: plonky2Circuit, + Proof: proofWithPis.Proof, + PublicInputs: proofWithPis.PublicInputs, + } + + proofWithPis2 := utils.DeserializeProofWithPublicInputs("./data/" + plonky2Circuit + "/proof_with_public_inputs.json") + witness := TestVerifierCircuit{ + plonky2CircuitName: plonky2Circuit, + Proof: proofWithPis2.Proof, + PublicInputs: proofWithPis2.PublicInputs, + } + + assert.ProverSucceeded( + &circuit, + &witness, + test.WithBackends(backend.GROTH16), + test.WithCurves(ecc.BN254), + test.NoFuzzing(), + test.NoSerialization(), + ) +} + +type testCircuit struct { + Arr [2]emulated.Element[emulated.Secp256k1Fp] + Expected emulated.Element[emulated.Secp256k1Fp] +} + +func (circuit *testCircuit) Define(api frontend.API) error { + field, _ := emulated.NewField[emulated.Secp256k1Fp](api) + + mulRes := field.Mul(&circuit.Arr[0], &circuit.Arr[1]) + field.AssertIsEqual(mulRes, &circuit.Expected) + + return nil +} + +func TestMain(t *testing.T) { + assert := test.NewAssert(t) + + var circuit testCircuit + + assert.ProverSucceeded( + &circuit, + &testCircuit{ + Arr: [2]emulated.Element[emulated.Secp256k1Fp]{ + emulated.ValueOf[emulated.Secp256k1Fp](42), + emulated.ValueOf[emulated.Secp256k1Fp](24), + }, + Expected: emulated.ValueOf[emulated.Secp256k1Fp](1008), + }, + test.WithBackends(backend.GROTH16), + test.WithCurves(ecc.BN254), + test.NoFuzzing(), + test.NoSerialization(), + ) +}