one := \!f? xs . %unit? xs () [ x := car xs . f? x (cons x ()) (one f? (cdr xs)) ];

l := 0;
r := 1;
d := 2;

left  := \!xs . map (one (eq? l)) (cdr xs);
right := \!xs . cons () (map (one (eq? r)) xs);
down  := \!xs . map (one (eq? d)) xs;

merge := \!xs !ys . %unit? xs ()
                              (%unit? ys xs
                                         (cons (append (car xs) (car ys))
                                               (merge (cdr xs) (cdr ys))));

next := \mask . merge (merge (down mask) (left mask)) (right mask);

fill := \!xs . %unit? xs () [ x := car xs; xs' := cdr xs . append (lrd x xs') (map (cons x) (fill xs')) ];

lrd := \!xs !ys . %unit? xs (cons (cons (cons l (cons r (cons d ()))) ys) ()) ();

solve := \!n mask . %zero? n (cons () ()) (concatMap (sol (%pred n)) (fill mask));

sol := \!n row . map (cons row) (solve n (next row));

nqueens := \!n . length (solve n (replicate n ()));

main := nqueens 7;