% Six by six chessboard problem, see "http://www.perlmonks.org/?node_id=821272"
% Logical programming variant

row(R) :- length(R, 6), rowpart(6, R).
rowpart(T, R) :- rowpart(3, 3, T, R).
rowpart(X, Y, 0, _) :- 0 =< X, 0 =< Y.
rowpart(X, Y, T, [b | R]) :- succ(Xp, X), succ(Tp, T), rowpart(Xp, Y, Tp, R).
rowpart(X, Y, T, [w | R]) :- succ(Yp, Y), succ(Tp, T), rowpart(X, Yp, Tp, R).

board(B) :-
	B = [R0, R1, R2, R3, R4, R5],
	for(lambda(arg(R), length(R, 6)), B), 
	transpose(B, BT),
	row(R0),
	write(board_debug0([R0])), nl,
	row(R1),
	R0 \== R1,
	row(R2),
	for(lambda(arg(R), R \== R2), [R0, R1]),
	row(R3),
	for(lambda(arg(R), R \== R3), [R0, R1, R2]),
	for(lambda(arg(C), rowpart(5, C)), BT),
	row(R4),
	for(lambda(arg(R), R \== R4), [R0, R1, R2, R3]),
	for(lambda(arg(C), row(C)), BT),
	%row(R5), % automatically true
	for(lambda(arg(R), R \== R5), [R0, R1, R2, R3, R4]),
	iota(6, I6), 
	for(lambda(arg(M), (
		take(M, BT, CB), nth0(M, BT, C),
		for(lambda(arg(U), U \== C), CB))), 
	I6).

nboard(N) :-
	findall(x, board(_B), L),
	length(L, N).

main :-
	nboard(N), write(N), nl.	


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