template MultiMux3(n) {
    signal input c[n][8];  // Constants
    signal input s[3];   // Selector
    signal output out[n];

    signal a210[n];
    signal a21[n];
    signal a20[n];
    signal a2[n];

    signal a10[n];
    signal a1[n];
    signal a0[n];
    signal a[n];

    // 4 constrains for the intermediary variables
    signal  s10;
    s10 <== s[1] * s[0];

    for (var i=0; i<n; i++) {

         a210[i] <==  ( c[i][ 7]-c[i][ 6]-c[i][ 5]+c[i][ 4] - c[i][ 3]+c[i][ 2]+c[i][ 1]-c[i][ 0] ) * s10;
          a21[i] <==  ( c[i][ 6]-c[i][ 4]-c[i][ 2]+c[i][ 0] ) * s[1];
          a20[i] <==  ( c[i][ 5]-c[i][ 4]-c[i][ 1]+c[i][ 0] ) * s[0];
           a2[i] <==  ( c[i][ 4]-c[i][ 0] );

          a10[i] <==  ( c[i][ 3]-c[i][ 2]-c[i][ 1]+c[i][ 0] ) * s10;
           a1[i] <==  ( c[i][ 2]-c[i][ 0] ) * s[1];
           a0[i] <==  ( c[i][ 1]-c[i][ 0] ) * s[0];
            a[i] <==  ( c[i][ 0] )

          out[i] <== ( a210[i] + a21[i] + a20[i] + a2[i] ) * s[2] +
                     (  a10[i] +  a1[i] +  a0[i] +  a[i] );

    }
}

template Mux3() {
    var i;
    signal input c[8];  // Constants
    signal input s[3];   // Selector
    signal output out;

    component mux = MultiMux3(1);

    for (i=0; i<8; i++) {
        mux.c[0][i] <== c[i];
    }

    for (i=0; i<3; i++) {
      s[i] ==> mux.s[i];
    }

    mux.out[0] ==> out;
}