ring R = 0,(x,y,z),(dp,c);
system("--min-time","0.001");
module M = [2*x + y - 2*z - 4, 2*x + y - 2*z, 2*x + 2*y + z + 2, -2*x - y - z - 1, 2*x - 2*y + z - 1, -2*x - 2*y + 2*z + 3], [-2*x + y + 1, 2*x - z + 1, 2*x + 2*y - 2*z - 2, 2*y - 2, x - 2*y + 2*z + 2, 2*x + 2*y - 2*z + 1];
timer = 0;
system("--ticks-per-sec",1000); // set timer resolution to ms
int t = timer;
t=timer; // initialize t by timer
module N = syz(transpose(M));
timer-t;

module M = [0, 2*x^2 + x*z + y^2 - 2*y*z - 2*y, -x^2 + 2*y*z + z^2 - 2*z + 3, 0, 2*x^2 + x*z + 2*y^2 - y*z + 2*z^2 + 1, -x^2 + y^2 + x + 3], [2*x^2 + x*y - y^2 + 2*y*z - z, x^2 + 2*x*y + 2*y*z + 2*z^2 - z - 2, -2*x*y - 2*y^2 + y*z - 1, 0, 2*x*z - y^2 + 2*y*z + z^2 - x + 1, 2*x*y - 2*x*z - z + 4];
timer = 0;
system("--ticks-per-sec",1000); // set timer resolution to ms
int t = timer;
t=timer; // initialize t by timer
module N = syz(transpose(M));
timer-t;

module M = [-x^2*z - y*z^2 - y^2 + x - 2*z, -2*x*y*z - 2*y^3 - y^2*z + 2*y*z^2 - 2*y*z - 1, x^2*z + x*y*z + y^2 + z, 0, 2*x^2*y - y^3 + y*z^2 + 2*x*z + 2*x + z + 1, x*z^2 - 2*y^3 + z^3 - 1], [x^2*y + 2*y^3 - x*z - y + 1, -x^2*z - x*y*z + y + 2, 0, y^3 + 2*y*z^2 - 2*x*y - 2*z^2 - 2*z + 1, y^2*z - x^2 + z + 1, x^3 + x*y*z - y^3 - 2*y*z - 2*x];
timer = 0;
system("--ticks-per-sec",1000); // set timer resolution to ms
int t = timer;
t=timer; // initialize t by timer
module N = syz(transpose(M));
timer-t;

module M = [y*z^3 + x^2*z + 2*y*z - 2*z^2 - z, -x*y*z^2 - 2*z^4 + 2*x*y - 2*x*z + y*z - 2, -2*y*z^3 + 2*x^2*z - y^3 + x*y + 1, 2*x^2*y^2 + 2*y^4 - 2*x^3 + 2*z^2 - 2, 0, -2*x^3*y + x*y^2*z - x*z^3 + y^2*z], [0, -x^2*y*z - z^4 + 2*x^3 - 3, -2*y^2*z^2 - 2*z^4 - 2*y^3 - y^2 + z + 1, 2*z^4 - 2*x^2*z - x*y*z - 2*y^2*z + 2, 0, 2*x^2*z^2 + 2*x*y^2*z - 2*y^2*z^2 + 2*x^2*z + x + 2];
timer = 0;
system("--ticks-per-sec",1000); // set timer resolution to ms
int t = timer;
t=timer; // initialize t by timer
module N = syz(transpose(M));
timer-t;

module M = [2*x*y - 2*y*z + x + y - 1, 2*x*z + 2*y^2 + z^2 + y - 4, x^2 - x*y + x*z - z^2 - 4, x^2 + 2*x*y + x*z - y^2 - z^2 + x - 1, x*y + z^2 + y - 4, x*y - 2*x*z + y*z - x - 1, -2*x*y - x*z - 2*x - z - 2, 2*x*y - 2*x*z + y^2 - 1], [x^2 + x*y - 2*x*z - 2*y^2 + 2*y*z + y - 2, 0, -x^2 + y^2 - 2*y*z - 2, x*y + 2*x - 2*z + 2, -2*x^2 + x*y - x*z + z^2 - z, x^2 + x*y - 2*x*z + 2*x - 3, 2*x*y + y^2 - 2*y*z + 2*z^2 + x + 2, x^2 - x*y + 2*x*z - y^2 - y*z - 2], [0, -x*y + 2*x*z - 2*y*z - 2*x + y - 2*z - 1, x*y + 2*y*z - 2*y + 2, 0, -x*y + 2*x*z - 2*y^2 + y*z + 2*z^2 + y, x^2 - x*y + 2*y^2 + 2*x - z + 4, -x*y + 3, -y*z + 2*z^2 + y - 1], [-x^2 + x*y + x*z - 2*z^2 - x + 1, y*z + 2*z^2 - x + y - z, 2*x*y + x*z + z^2, -2*x^2 - x*z + y^2 - y*z + 2*x - 2*z + 1, 2*x*z - 2*x + 2*y + 1, -2*x^2 + x*z - 2*y^2 + 2*y + z + 1, 0, -2*x^2 + 2*x*y + 2*y^2 - z^2 + 2*x + 2*z - 2];
timer = 0;
system("--ticks-per-sec",1000); // set timer resolution to ms
int t = timer;
t=timer; // initialize t by timer
module N = syz(transpose(M));
timer-t;

module M = [-2*x^2*y + 2*x*y*z + 2*y^2*z - 2*y*z^2 + z^3 + y*z - 1, -2*x^2*y - x*y^2 - 2*x*z^2 + 2*z^3 + x*z + z - 1, 0, 0, -2*x*y*z + y^3 - 2*z^3 + 2*x*y - 2, x^3 + y^2*z - y^2 + 1, 0, -x^2*z + 2*x*z^2 + 2*y*z^2 - z^3 - x*y + 2*z - 1], [-2*x^3 + y*z^2 - z^2 - 2*z - 4, -x*y*z - 2*y^2*z + y + 2, -2*x^3 - 2*x*y^2 - x^2 + 2*x*y - z + 2, x^2 + 2*y*z + 2*x - z - 2, 0, -2*x^3 + 2*x*z - z^2 + 1, 0, -2*x*y*z - y*z^2 - x + 2*y - 1], [0, 0, 2*x*y*z - y^2*z + 2*y*z^2 + y^2 + y*z + 2, 0, -2*x^2*y - 2*z^3 - x*z - y^2 - 1, 2*x^3 + x*y*z + y^3 + y^2*z + 2*x^2 - x*y + 1, -x^2*z - y*z^2 - y^2 + x - 2*z, -2*x*y*z - 2*y^3 - y^2*z + 2*y*z^2 - 2*y*z - 1], [x^2*z + x*y*z + y^2 + z, 0, 2*x^2*y - y^3 + y*z^2 + 2*x*z + 2*x + z + 1, x*z^2 - 2*y^3 + z^3 - 1, x^2*y + 2*y^3 - x*z - y + 1, -x^2*z - x*y*z + y + 2, 0, y^3 + 2*y*z^2 - 2*x*y - 2*z^2 - 2*z + 1];
timer = 0;
system("--ticks-per-sec",1000); // set timer resolution to ms
int t = timer;
t=timer; // initialize t by timer
module N = syz(transpose(M));
timer-t;

module M = [2*x^2 - y^2 + 2*x + 1, -y^2 + 2*x - y - 1, 0, 2*x^2 - x*y - y^2 + 2*x - y - 3, -x^2 - x*y + 2*y^2 + 2*x - 2*y - 1, 2*x^2 + 2*x*y + y^2 - x + 2*y + 1, 2*x*y - 2*y^2 + x - 1, x^2 + 2*x*y - y^2 + 2*x + y - 2, 2*x^2 - 2*x*y - 2*y^2 - y - 1, x^2 - y - 2], [-2*x^2 - 2*x*y + y^2 + 2*x - 2*y - 2, 0, 2*x*y - 2*y^2 + 2*x - y - 2, 0, x^2 - x*y - y + 3, 0, -x^2 - 2*x*y - y^2 + x - 2*y - 3, 0, -x^2 - 2*x*y + y^2 + x + 2, -x^2 + x*y + 2*y^2 - x - 2*y - 3], [2*x^2 - 2*x*y - 2*y^2 - 2*x - y - 2, 2*x^2 - 2*x*y - x + 1, 0, 0, -2*x^2 - 2*x*y - y^2 + x + 2*y - 3, 2*x^2 + x*y - y^2 + x - 2*y + 1, x^2 + x*y + y^2 - 2*x, -x^2 + 2*y^2 - x - y - 2, -x*y - x + 2*y, 0], [0, -x*y - y^2 - x - 3, x^2 - x*y - 2*y^2 - 2*y - 1, 0, x^2 - x*y - 2*y^2 - 2*x - 2, 2*x^2 - x*y - y^2 - 2*x + 2*y, 0, 2*x^2 - x*y + y^2 - 2*x + 1, -2*x*y + 2*y^2 - y + 1, 0], [x^2 - x*y - y^2 + x - 2*y + 4, 2*x*y + 2*y^2 + 2*x + y, -2*x^2 - 2*y^2 - 2*x + 3, 0, -2*x^2 + 2*x*y + y^2 - x - 2*y + 2, x^2 - 2*y^2 + x, -2*x^2 + 2*x*y + 2*y^2 - x + 2*y - 3, 2*y^2 - x + y - 1, x^2 + x*y - y^2 - 2*x + 2*y + 3, 0], [0, x^2 + 2*y^2 + x + y, -x^2 - x*y - x + y + 3, -x^2 - 2*y^2 - 2*x + 2*y + 1, -2*x*y - y^2 - 2*x - 2*y + 1, -2*x^2 + 2*x*y + 2*y^2 - 2*y, -x^2 + 2*x*y - y^2 + y, -x^2 + x*y + 2*y^2 - 2*y - 2, -2*x*y - y^2 - x - y + 2, 0];
timer = 0;
system("--ticks-per-sec",1000); // set timer resolution to ms
int t = timer;
t=timer; // initialize t by timer
module N = syz(transpose(M));
timer-t;


module M = [-2*x*y^2 + x*y - y^2 - 3, x^2*y + 2*x^2 + x*y + 2*y^2 - y - 1, x^3 + 2*x^2*y - 2*x - y + 4, -2*x^3 + 2*x^2*y + 2*y^3 - x*y + y^2 + 2, x^3 - 2*x^2*y - 2*y^2 - x + 2*y - 2, -x^3 + x^2*y + x*y^2 - 2*y^3 - 2*x^2 - x*y, -x^3 + 2*x*y^2 - x - 2*y - 1, 0, x*y + y^2 - 2*y - 1, 0], [x^3 - x^2*y + x^2 + x*y + x + 1, x*y^2 + x^2 + x*y + 2*x, x*y^2 + 2*x^2 - 2*x*y - 2, 2*y^3 - 2, 0, -2*y^3 + 2*x^2 - 2*y^2 + 2*y + 3, 0, x^3 + 2*x^2*y - 2*x*y^2 - y^3 + 2*x*y + 3, 0, 0], [x^3 - y^3 + x^2 + 2*x*y - 2*y^2 - 2*y - 2, 2*x^3 + x*y^2 + 2*x*y - x + 1, 2*x^2*y + 2*y^2 + 2*x - y + 3, 2*x^3 - 2*y^3 + x*y + 2, -x^2*y - 2*x*y^2 + 2*x*y - 2*x - y + 1, 0, -x^3 + 2*x*y^2 - 2*x^2 + x - 2*y - 2, 2*x^3 + 2*y^3 + x*y - 2*y - 1, 0, 0], [x^3 - x*y^2 + x^2 - 2*x*y - y^2 + 2, 0, 0, 2*y^3 - 2*x^2 + 2*y + 2, -x^2*y + x^2 + x*y - 2*y^2 + x - 1, 2*x*y^2 - 2*x - 4, 0, x^2*y - y^3 + 2*x^2 + 2*x + 1, -x^3 + 2*x*y^2 - x^2 - 2*x - 2, -x^3 - x^2*y - 2*x*y - 2*y - 1], [0, 0, 2*x^3 + x^2*y - x^2 - 2*x - 1, 2*x^2*y + x*y^2 + x*y + y^2 - 3, -x^2 - 2*x*y + 2*y^2 - 2*y - 1, 2*x^3 + 2*x*y - y^2 - 2*x - 1, x*y^2 + x^2 - 2*y^2 + 2*x - 3, 0, -2*x^3 + 2*x*y^2 - 2*y^3 + 2*x*y + 2*y + 1, -2*x*y^2 - 2*x^2 + 2*y^2 + x - 3], [0, -x^3 - x^2*y + y^3 - 2*x - 2*y + 1, x^3 + x^2*y + 2*y^3 - 2*x + y - 2, 2*x^2*y + 2*x*y^2 + 2*x^2 + 2*x - 2*y + 2, -2*x*y^2 - 2*y^3 + 2*x^2 + x*y, -x^3 - x*y^2 - y^3 - x*y + 2*x + y, 2*x*y^2 + 2*x*y - 2*y^2 + 3, x^3 + 2*y^3 + x^2 - y^2 - 2*y + 1, 2*x^3 + x^2 - 2*x*y + x - 1, -2*x^3 + x^2*y + 2*x*y^2 - 2*y^2 - y];
timer = 0;
system("--ticks-per-sec",1000); // set timer resolution to ms
int t = timer;
t=timer; // initialize t by timer
module N = syz(transpose(M));
timer-t;