from __future__ import print_function, division

import itertools

import a9bsp

n_queens = a9bsp.AccessibleBSP()

# Number of queens and board size; NxN board with N queens.
queen_count = 8

# Generate a chess board with each cell represented by an X and Y position.
chess_board = itertools.product(range(queen_count), range(queen_count))

# Define the conditions of the problem. Iterate through every square on the
# board and compare it with every other square on the board.
for (ax, ay), (bx, by) in itertools.combinations(chess_board, 2):

                                            # Two queens cannot:
    if ((ax == bx) or                       # - Be in the same column
        (ay == by) or                       # - Be in the same row
        (abs((ay - by) / (ax - bx)) == 1)): # - Be on the same diagonal

        # Therefore, two queens cannot be in any pairs of cells meeting
        # these conditions.
        n_queens.mutually_excludes([(ax, ay), (bx, by)])

# One queen per column
for row in range(queen_count):
    squares_in_column = [(n, row) for n in range(queen_count)]
    n_queens.includes_any(squares_in_column)

# One queen per row
for column in range(queen_count):
    squares_in_row = [(column, n) for n in range(queen_count)]
    n_queens.includes_any(squares_in_row)

# Print a board with the positions of each queen
for n, solution in enumerate(n_queens.solutions, 1):
    print("Solution %d:" % (n,))
    for y in range(queen_count):
        for x in range(queen_count):
            if (x, y) in solution:
                print("Q ", end="")
            else:
                print(". ", end="")
        print("")

Solution 1:
. . Q . . . . .
. . . . Q . . .
. Q . . . . . .
. . . . . . . Q
. . . . . Q . .
. . . Q . . . .
. . . . . . Q .
Q . . . . . . .