rainbow previous h = -1;

rainbow(h) = {
	my (h = floor(h*3600) % 3600);
	if (rainbow previous h != h,
		print ("color ", h\10, ".", h%10, ":1:.5");
		rainbow previous h = h;
	);
}

paint(c) = rainbow(lift(Mod(67,359)*c)/359);

allocate mem(2^30)

W = 1000
T = matrix(W,W, i,j, -1)
hori = vector(W)
vert = vector(W)
dia1 = vector(2*W+1)
dia2 = vector(2*W+1)

get(z) = {
	if (real(z)<1 || real(z)>W || imag(z)<1 || imag(z)>W,
		return (-1),
		return (T[real(z),imag(z)]);
	);
}

{
	for (d=1, W,
		for (x=1, d,
			y=d+1-x;
			z=x+I*y;

			my (h=imag(z),
				w=real(z),
				d1=real(z)+imag(z)-1,
				d2=real(z)-imag(z)+W,
				seen=bitor(bitor(hori[h], vert[w]),
						   bitor(dia1[d1], dia2[d2])));

			\\ 8 knight moves
			for (k=0, 7,
				my (kz = z + (2+I*(-1)^(k%2)) * I^(k\2), o=get(kz));
				if (o>=0,
					seen = bitor(seen, 2^o);
				);
			);

			my (v=valuation(seen+1,2));

			hori[h]  += 2^v;
			vert[w]  += 2^v;
			dia1[d1] += 2^v;
			dia2[d2] += 2^v;

			T[x,y] = v;

			if (y==1,
				print (x-1 " " v);
			);
		);
	);
}

quit