# Find combinations of a certain size
def combine (a, b, lo, size):
  hi = len(a)
  if (lo == hi):
    if (len(b) == size):
      print (b)
    return
  if (len (b) == size):
    print (b)
  else:
    c = b[:]
    b.append (a[lo])
    combine (a, b, lo + 1, size)
    combine (a, c, lo + 1, size)
 
def main():
  a = ['A', 'B', 'C', 'D', 'E', 'F']
  b = []
  combine (a, b, 0, 6)

main()

# solve the 8 Queens problem using back tracking
class Queens (object):
  # initialize the board
  def __init__ (self, n = 8):
    self.board = []
    self.n = n
    for i in range (self.n):
      row = []
      for j in range (self.n):
        row.append ("*")
      self.board.append (row)

  # check if no queen captures another
  def is_valid (self, row, col):
    for i in range (self.n):
      if (self.board[row][i] == 'Q' or self.board[i][col] == 'Q'):
        return False
    for i in range (self.n):
      for j in range (self.n):
        row_diff = abs (row - i)
        col_diff = abs (col - j)
        if (row_diff == col_diff) and (self.board[i][j] == 'Q'):
          return False
    return True

  # print the board
  def print_board (self):
    for i in range (self.n):
      for j in range (self.n):
        print (self.board[i][j], end = ' ')
      print()

  # do a recursive solution to the problem
  def recursive_solve (self, col):
    if (col == self.n):
      return True
    else:
      for i in range (self.n):
        if (self.is_valid (i, col)):
          self.board[i][col] = 'Q'
          if (self.recursive_solve (col + 1)):
            return True
          self.board[i][col] = '*'
      return False
 
  # if the problem has a solution print the board
  def solve (self):
    for i in range (self.n):
      if (self.recursive_solve (i)):
        self.print_board ()
	
def main():
  # create an object
  game = Queens (8)
  game.solve()

main()