int: n;
% La reina de la i columna está en la fila q[i]
array [1..n] of var 1..n: q;

include "alldifferent.mzn";

% Filas distintas.
constraint alldifferent(q);

% Diagonales distintas.
constraint alldifferent([ q[i] + i | i in 1..n]);

% Hacia arriba + hacia abajo.
constraint alldifferent([ q[i] - i | i in 1..n]);

include "lex_lesseq.mzn";

% Modelo booleano alternativo:
% Mapa de cada posición i, j a un número booleano
% señalando si hay una reina en la posición i, j.
array[1..n,1..n] of var bool: qb;

% Coeficiente de canalización.
constraint forall (i,j in 1..n) ( qb[i,j] <-> (q[i]=j) );

% Restricciones de ruptura de simetría lexicográfica.
constraint
    lex_lesseq(array1d(qb), [ qb[j,i] | i,j in 1..n ])
/\  lex_lesseq(array1d(qb), [ qb[i,j] | i in reverse(1..n), j in 1..n ])
/\  lex_lesseq(array1d(qb), [ qb[j,i] | i in 1..n, j in reverse(1..n) ])
/\  lex_lesseq(array1d(qb), [ qb[i,j] | i in 1..n, j in reverse(1..n) ])
/\  lex_lesseq(array1d(qb), [ qb[j,i] | i in reverse(1..n), j in 1..n ])
/\  lex_lesseq(array1d(qb), [ qb[i,j] | i,j in reverse(1..n) ])
/\  lex_lesseq(array1d(qb), [ qb[j,i] | i,j in reverse(1..n) ])
;

% Búsqueda.
solve :: int_search(q, first_fail, indomain_min, complete)
      satisfy;
output [ if fix(q[j]) == i then "Q" else "." endif ++
         if j == n then "\n" else "" endif | i,j in 1..n]