






"""simple docstring"""



from __future__ import annotations

from random import random






class 							__SCREAMING_SNAKE_CASE						:


							def __init__(			self      :						Union[str, Any]			,    snake_case      :						int | None = None							):
													'''simple docstring'''





													A__						:  Dict		  =  value
													A__						:  Tuple		  =  random()
													A__						:  Node | None		  =  None
													A__						:  Node | None		  =  None


							def __repr__(			self      :						Optional[Any]							):
													'''simple docstring'''





													from pprint import pformat

													if self.left is None and self.right is None:
																			return F'\'{self.value}: {self.prior:.5}\''
													else:
																			return pformat(
																			    {F'{self.value}: {self.prior:.5}': (self.left, self.right)}			,    indent=1							)


							def __str__(			self      :						Union[str, Any]							):
													'''simple docstring'''





													A__						:  List[Any]		  =  str(self.value							) + """ """
													A__						:  List[Any]		  =  str(self.left or """"""							)
													A__						:  List[Any]		  =  str(self.right or """"""							)
													return value + left + right




def      _lowerCAmelCase		(							UpperCAmelCase__       :					Node | None,						UpperCAmelCase__       :					int      )		->tuple[Node | None, Node | None]:
						if root is None:  # None tree is split into 2 Nones
												return None, None
						elif root.value is None:
												return None, None
						else:
												if value < root.value:
																		A__						:  Dict		  =  split(root.left,						UpperCAmelCase__      )
																		return left, root
												else:
																		A__						:  Any		  =  split(root.right,						UpperCAmelCase__      )
																		return root, right




def      _lowerCAmelCase		(							UpperCAmelCase__       :					Node | None,						UpperCAmelCase__       :					Node | None      )		->Node | None:
						if (not left) or (not right):  # If one node is None, return the other
												return left or right
						elif left.prior < right.prior:
												A__						:  Optional[Any]		  =  merge(left.right,						UpperCAmelCase__      )
												return left
						else:
												A__						:  Dict		  =  merge(UpperCAmelCase__,						right.left      )
												return right




def      _lowerCAmelCase		(							UpperCAmelCase__       :					Node | None,						UpperCAmelCase__       :					int      )		->Node | None:
						A__						:  Union[str, Any]		  =  Node(UpperCAmelCase__      )
						A__						:  List[str]		  =  split(UpperCAmelCase__,						UpperCAmelCase__      )
						return merge(merge(UpperCAmelCase__,						UpperCAmelCase__      ),						UpperCAmelCase__      )




def      _lowerCAmelCase		(							UpperCAmelCase__       :					Node | None,						UpperCAmelCase__       :					int      )		->Node | None:
						A__						:  Optional[int]		  =  split(UpperCAmelCase__,						value - 1      )
						A__						:  List[Any]		  =  split(UpperCAmelCase__,						UpperCAmelCase__      )
						return merge(UpperCAmelCase__,						UpperCAmelCase__      )




def      _lowerCAmelCase		(							UpperCAmelCase__       :					Node | None      )		->None:
						if not root:  # None
												return
						else:
												inorder(root.left      )
												print(root.value,						end=""","""      )
												inorder(root.right      )




def      _lowerCAmelCase		(							UpperCAmelCase__       :					Node | None,						UpperCAmelCase__       :					str      )		->Node | None:
						for arg in args.split():
												if arg[0] == "+":
																		A__						:  int		  =  insert(UpperCAmelCase__,						int(arg[1:]      )      )

												elif arg[0] == "-":
																		A__						:  Dict		  =  erase(UpperCAmelCase__,						int(arg[1:]      )      )

												else:
																		print("""Unknown command"""      )

						return root




def      _lowerCAmelCase		(							)		->None:
						A__						:  Union[str, Any]		  =  None
						print(
						    """enter numbers to create a tree, + value to add value into treap, """
						    """- value to erase all nodes with value. 'q' to quit. """      )

						A__						:  int		  =  input()
						while args != "q":
												A__						:  Dict		  =  interact_treap(UpperCAmelCase__,						UpperCAmelCase__      )
												print(UpperCAmelCase__      )
												A__						:  List[Any]		  =  input()

						print("""good by!"""      )


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						main()














"""simple docstring"""



from __future__ import annotations

A_    =							[]




def      _lowerCAmelCase		(							UpperCAmelCase__       :					list[list[int]],						UpperCAmelCase__       :					int,						UpperCAmelCase__       :					int      )		->bool:
						for i in range(len(UpperCAmelCase__      )      ):
												if board[row][i] == 1:
																		return False
						for i in range(len(UpperCAmelCase__      )      ):
												if board[i][column] == 1:
																		return False
						for i, j in zip(range(UpperCAmelCase__,						-1,						-1      ),						range(UpperCAmelCase__,						-1,						-1      )      ):
												if board[i][j] == 1:
																		return False
						for i, j in zip(range(UpperCAmelCase__,						-1,						-1      ),						range(UpperCAmelCase__,						len(UpperCAmelCase__      )      )      ):
												if board[i][j] == 1:
																		return False
						return True




def      _lowerCAmelCase		(							UpperCAmelCase__       :					list[list[int]],						UpperCAmelCase__       :					int      )		->bool:
						if row >= len(UpperCAmelCase__      ):
												solution.append(UpperCAmelCase__      )
												printboard(UpperCAmelCase__      )
												print()
												return True
						for i in range(len(UpperCAmelCase__      )      ):
												if is_safe(UpperCAmelCase__,						UpperCAmelCase__,						UpperCAmelCase__      ):
																		A__						:  Tuple		  =  1
																		solve(UpperCAmelCase__,						row + 1      )
																		A__						:  Optional[int]		  =  0
						return False




def      _lowerCAmelCase		(							UpperCAmelCase__       :					list[list[int]]      )		->None:
						for i in range(len(UpperCAmelCase__      )      ):
												for j in range(len(UpperCAmelCase__      )      ):
																		if board[i][j] == 1:
																								print("""Q""",						end=""" """      )
																		else:
																								print(""".""",						end=""" """      )
												print()


# n=int(input("The no. of queens"))
A_    =							8
A_    =							[[0 for i in range(n)] for j in range(n)]
solve(board, 0)

print('''The total no. of solutions are :''', len(solution))






