import sat.
% import mip.

queens_sat(N,Q) =>
  Q = new_array(N,N),
  Q :: 0..1,

  foreach (K in 1-N..N-1)
    sum([Q[I,J] : I in 1..N, J in 1..N, I-J==K]) #=< 1
  end,

  foreach (K in 2..2*N)
    sum([Q[I,J] :  I in 1..N, J in 1..N, I+J==K]) #=< 1
  end,

  foreach (I in 1..N)
    sum([Q[I,J] : J in 1..N]) #= 1
  end,

  foreach (J in 1..N)
    sum([Q[I,J] : I in 1..N]) #= 1
  end,
  solve([inout],Q).