template XOR() {
    signal input a;
    signal input b;
    signal output out;

    out <== a + b - 2*a*b;
}

template AND() {
    signal input a;
    signal input b;
    signal output out;

    out <== a*b;
}

template OR() {
    signal input a;
    signal input b;
    signal output out;

    out <== a + b - a*b;
}

template NOT() {
    signal input in;
    signal output out;

    out <== 1 + in - 2*in;
}

template NAND() {
    signal input a;
    signal input b;
    signal output out;

    out <== 1 - a*b;
}

template NOR() {
    signal input a;
    signal input b;
    signal output out;

    out <== a*b + 1 - a - b;
}