"""simple docstring"""



from __future__ import annotations






class 				snake_case__     :


 def __init__(				self  ,						lowerCamelCase		):
        __a     				=  data
        __a     				=  None
        __a     				=  None



def 					_lowerCamelCase(					a							):  # In Order traversal of the tree
       if tree:
              display(tree.left							)
              print(tree.data							)
              display(tree.right							)



def 					_lowerCamelCase(					a							):
       return 1 + max(depth_of_tree(tree.left							) ,  depth_of_tree(tree.right							)							) if tree else 0



def 					_lowerCamelCase(					a							):
       if not tree:
              return True
       if tree.left and tree.right:
              return is_full_binary_tree(tree.left							) and is_full_binary_tree(tree.right							)
       else:
              return not tree.left and not tree.right



def 					_lowerCamelCase(					):  # Main function for testing.
       __a     				=  Node(1							)
       __a     				=  Node(2							)
       __a     				=  Node(3							)
       __a     				=  Node(4							)
       __a     				=  Node(5							)
       __a     				=  Node(6							)
       __a     				=  Node(7							)
       __a     				=  Node(8							)
       __a     				=  Node(9							)

       print(is_full_binary_tree(a							)							)
       print(depth_of_tree(a							)							)
       print("Tree is: "							)
       display(a							)


if __name__ == "__main__":
   main()

"""simple docstring"""



from __future__ import annotations



def 					_lowerCamelCase(					a ,  a ,  a ,  a ,  a ,  ):
       __a     				=  len(a							)

       # If row is equal to the size of the board it means there are a queen in each row in
       # the current board (possible_board)
       if row == n:
              # We convert the variable possible_board that looks like this: [1, 3, 0, 2] to
              # this: ['. Q . . ', '. . . Q ', 'Q . . . ', '. . Q . ']
              boards.append([". " * i + "Q " + ". " * (n - 1 - i) for i in possible_board]							)
              return

       # We iterate each column in the row to find all possible results in each row
       for col in range(a							):
              # We apply that we learned previously. First we check that in the current board
              # (possible_board) there are not other same value because if there is it means
              # that there are a collision in vertical. Then we apply the two formulas we
              # learned before:
              #
              # 45º: y - x = b or 45: row - col = b
              # 135º: y + x = b or row + col = b.
              #
              # And we verify if the results of this two formulas not exist in their variables
              # respectively.  (diagonal_right_collisions, diagonal_left_collisions)
              #
              # If any or these are True it means there is a collision so we continue to the
              # next value in the for loop.
              if (
                  col in possible_board
                  or row - col in diagonal_right_collisions
                  or row + col in diagonal_left_collisions
              ):
                     continue

              # If it is False we call dfs function again and we update the inputs
              depth_first_search(
                  [*possible_board, col] ,  [*diagonal_right_collisions, row - col] ,  [*diagonal_left_collisions, row + col] ,  a ,  a ,  )



def 					_lowerCamelCase(					a							):
       __a     				=  []
       depth_first_search([] ,  [] ,  [] ,  a ,  a							)

       # Print all the boards
       for board in boards:
              for column in board:
                     print(a							)
              print(""							)

       print(len(a							) ,  "solutions were found."							)


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   n_queens_solution(4)
