w max = 2500

hor = vector(2*w max + 1)
dia = vector(#hor)
ant = vector(#hor)

len = [  0, -1,  0,  0,  0,  0 ]
dx  = [ +2, +1, -1, -2, -1, +1 ]
dy  = [  0, +1, +1,  0, -1, -1 ]

n = -1;
visit(x,y) = {
	my (h=w max + 1 + y);
	my (d=w max + 1 + (x+y)/2);
	my (a=w max + 1 + (x-y)/2);

	my (mask = bitor(hor[h], bitor(dia[d], ant[a])));
	my (v = valuation(mask+1,2));

	if (y>=0 && x==-y,
		print (n++ " " v);
	);

	my (p=2^v);

	hor[h] += p;
	dia[d] += p;
	ant[a] += p;
}

{
	x = 0;
	y = 0;
	visit(x,y);
	for (w=1, w max,
		for (s=1, #len,
			for (i=1, w+len[s],
				x += dx[s];
				y += dy[s];
				visit(x,y);
			);
		);
	);
}

quit