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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.



def queens(n): # n: size of the chess board

   p = pymprog.model('queens')

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

   x = p.var(iboard, 'X', 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.max(sum(x[t] for t in iboard), 'queens')

   return p,x



n = raw_input("board size = ")

n = int(n)

p,x = queens(n)

ys = raw_input("Would you like to place a queen? [y]/n")

while ys!='n':

   r = raw_input("row [0, %i): "%n)

   c = raw_input("col [0, %i): "%n)

   p.st(x[int(r), int(c)] == 1)

   ys = raw_input("Would you like to place another queen? [y]/n")

 

p.solve(int)

#print "solver status: ", p.p.status

for i in range(n):

   for j in range(n):

       if x[i,j].primal > 0.5: print 'Q',

       else: print '.',

   print