function c = count_colorings(n, piece, eqRels)

[l, w] = size(piece);
[Adj, numb] = adjacency(piece);
% Adj = Adj|(Adj')|eye(n);

%Check symmetries
sym = 1:n;
%flip vert
if piece == piece(l:-1:1, :)
    sym = [sym; sym_perm(n, numb, numb(l:-1:1, :))];
end
%flip horiz
if piece == piece(:, w:-1:1)
    sym = [sym; sym_perm(n, numb, numb(:, w:-1:1))];
end
%rotate 180
if piece == (piece(l:-1:1, w:-1:1))
    sym = [sym; sym_perm(n, numb, numb(l:-1:1, w:-1:1))];
end
if l == w
    p2 = piece';
    n2 = numb';
    %flip across main diagonal
    if piece == p2
        sym = [sym; sym_perm(n, numb, n2)];
    end
    %rotate 90
    if piece == p2(l:-1:1, :)
        sym = [sym; sym_perm(n, numb, n2(l:-1:1, :)); sym_perm(n, n2(l:-1:1, :), numb)];
    end
    %flip across antidiagonal
    if piece == p2(l:-1:1, w:-1:1)
        sym = [sym; sym_perm(n, numb, n2(l:-1:1, w:-1:1))];
    end
end
s = size(sym, 1);

c = 0;
relCount = size(eqRels, 3);
for k = 1:relCount
    er = eqRels(:, :, k);
    er = er|(er')|eye(n);
    if (er&Adj) == 0
        %coloring works
        c = c + 1;
        for j = 2:s
            perm = sym(j, :);
            er2 = er(perm, perm);
            if er == er2
                %coloring is preserved by this permutation
                c = c + 1;
            end
        end
    end
end
c = c/s;