{-# LANGUAGE NoImplicitPrelude #-}

import Prelude (print)
import Set

nqueens n = (nqueens' empty zero (range n))
  where
  compatible xa ya b = xa + ya /= xb + yb && xa + yb /= xb + ya
    where xb = fst b
          yb = snd b
  nqueens' sol y xs = iif (y == n) sol (
    any (\x -> nqueens' (sol << pair x y) (succ y) (xs >> x))
    (filter (\x -> all (compatible x y) sol) xs) )

nqueensAll n = (nqueensAll' empty zero (range n))
  where
  compatible xa ya b = xa + ya /= xb + yb && xa + yb /= xb + ya
    where xb = fst b
          yb = snd b
  nqueensAll' sol y xs = iif (y == n) (singleton sol) (
    flatmap (\x -> nqueensAll' (sol << pair x y) (succ y) (xs >> x))
    (filter (\x -> all (compatible x y) sol) xs) )

-- verify there are 14,200 solutions for n = 12
main = print (size (nqueensAll twelve) == (ten * ten + six * seven) * ten * ten)