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from __future__ import print_function

import pymprog



# The Queens Problem is to place as many queens as possible on the nxn

#   chess board in a way that they do not fight

#   each other. This problem is probably as old as the chess game itself,

#   and thus its origin is not known, but it is known that Gauss studied

#   this problem.



n = 16 #size of chess board

p = pymprog.model('queens')

iboard = pymprog.iprod(range(n), range(n)) #create indices

x = p.var('X', iboard, bool) #create variables

#row wise:

p.st([sum(x[i,j] for j in range(n)) <= 1 for i in range(n)])

#column wise:

p.st([sum(x[i,j] for i in range(n)) <= 1 for j in range(n)])

#diagion '/' wise

p.st([sum(x[i,j] for i,j in iboard if i-j == k) <= 1 

                    for k in range(2-n, n-1)])

#diagion '\' wise

p.st([sum(x[i,j] for i,j in iboard if i+j == k) <= 1 

                    for k in range(1, n+n-2)])

p.maximize(sum(x[t] for t in iboard), 'queens')



p.solve()

for i in range(n):

   for j in range(n):

       if x[i,j].primal > 0: print('Q', end=' ')

       else: print('.', end=' ')

   print()

p.end()