






"""simple docstring"""

from math import factorial

class 						A_							:







				def __init__(							self							:						Dict						,    __lowerCamelCase							:						Union[str, Any]						,    __lowerCamelCase							:						int	)				->					Tuple:
										__magic_name__            =     real
										if isinstance(__lowerCamelCase						,    __lowerCamelCase	):
																__magic_name__            =     [1] * rank
										else:
																__magic_name__            =     rank







				def __repr__(							self							:						Any	)				->					List[Any]:
										return (
										    f'''{self.real}+'''
										    f'''{"+".join(str(__lowerCamelCase	)+"E"+str(n+1	)for n,dual in enumerate(self.duals	)	)}'''
										)







				def     _snake_case					(							self							:						Optional[Any]	)				->					Union[str, Any]:
										__magic_name__            =     self.duals.copy()
										while cur[-1] == 0:
																cur.pop(-1	)
										return Dual(self.real						,    __lowerCamelCase	)







				def __add__(							self							:						Union[str, Any]						,    __lowerCamelCase							:						str	)				->					Dict:
										if not isinstance(__lowerCamelCase						,    __lowerCamelCase	):
																return Dual(self.real + other						,    self.duals	)
										__magic_name__            =     self.duals.copy()
										__magic_name__            =     other.duals.copy()
										if len(__lowerCamelCase	) > len(__lowerCamelCase	):
																o_dual.extend([1] * (len(__lowerCamelCase	) - len(__lowerCamelCase	))	)
										elif len(__lowerCamelCase	) < len(__lowerCamelCase	):
																s_dual.extend([1] * (len(__lowerCamelCase	) - len(__lowerCamelCase	))	)
										__magic_name__            =     []
										for i in range(len(__lowerCamelCase	)	):
																new_duals.append(s_dual[i] + o_dual[i]	)
										return Dual(self.real + other.real						,    __lowerCamelCase	)

				UpperCAmelCase__        =				__add__







				def __sub__(							self							:						List[Any]						,    __lowerCamelCase							:						Any	)				->					str:
										return self + other * -1







				def __mul__(							self							:						List[Any]						,    __lowerCamelCase							:						Any	)				->					int:
										if not isinstance(__lowerCamelCase						,    __lowerCamelCase	):
																__magic_name__            =     []
																for i in self.duals:
																						new_duals.append(i * other	)
																return Dual(self.real * other						,    __lowerCamelCase	)
										__magic_name__            =     [0] * (len(self.duals	) + len(other.duals	) + 1)
										for i, item in enumerate(self.duals	):
																for j, jtem in enumerate(other.duals	):
																						new_duals[i + j + 1] += item * jtem
										for k in range(len(self.duals	)	):
																new_duals[k] += self.duals[k] * other.real
										for index in range(len(other.duals	)	):
																new_duals[index] += other.duals[index] * self.real
										return Dual(self.real * other.real						,    __lowerCamelCase	)

				UpperCAmelCase__        =				__mul__







				def __truediv__(							self							:						Union[str, Any]						,    __lowerCamelCase							:						Optional[int]	)				->					Optional[int]:
										if not isinstance(__lowerCamelCase						,    __lowerCamelCase	):
																__magic_name__            =     []
																for i in self.duals:
																						new_duals.append(i / other	)
																return Dual(self.real / other						,    __lowerCamelCase	)
										raise ValueError







				def __floordiv__(							self							:						str						,    __lowerCamelCase							:						Dict	)				->					Any:
										if not isinstance(__lowerCamelCase						,    __lowerCamelCase	):
																__magic_name__            =     []
																for i in self.duals:
																						new_duals.append(i // other	)
																return Dual(self.real // other						,    __lowerCamelCase	)
										raise ValueError







				def __pow__(							self							:						Optional[int]						,    __lowerCamelCase							:						Dict	)				->					Any:
										if n < 0 or isinstance(__lowerCamelCase						,    __lowerCamelCase	):
																raise ValueError("power must be a positive integer"	)
										if n == 0:
																return 1
										if n == 1:
																return self
										__magic_name__            =     self
										for _ in range(n - 1	):
																x *= self
										return x






def _lowerCAmelCase	(  __lowerCamelCase:List[str] ,						__lowerCamelCase:List[str] ,						__lowerCamelCase:str   ):

						'''simple docstring'''






						if not callable(__lowerCamelCase   ):
												raise ValueError("differentiate() requires a function as input for func"   )
						if not isinstance(__lowerCamelCase ,						(float, int)   ):
												raise ValueError("differentiate() requires a float as input for position"   )
						if not isinstance(__lowerCamelCase ,						__lowerCamelCase   ):
												raise ValueError("differentiate() requires an int as input for order"   )
						__magic_name__            =     Dual(__lowerCamelCase ,						1   )
						__magic_name__            =     func(__lowerCamelCase   )
						if order == 0:
												return result.real
						return result.duals[order - 1] * factorial(__lowerCamelCase   )


if __name__ == "__main__":
			import doctest

			doctest.testmod()






			def _lowerCAmelCase	(  __lowerCamelCase:Any   ):

									'''simple docstring'''






									return y**2 * y**4


			print(differentiate(f, 9, 2))











"""simple docstring"""

from __future__ import annotations

lowercase    			=       []






def _lowerCAmelCase	(  __lowerCamelCase:list[list[int]] ,						__lowerCamelCase:int ,						__lowerCamelCase:int   ):

						'''simple docstring'''






						for i in range(len(__lowerCamelCase   )   ):
												if board[row][i] == 1:
																		return False
						for i in range(len(__lowerCamelCase   )   ):
												if board[i][column] == 1:
																		return False
						for i, j in zip(range(__lowerCamelCase ,						-1 ,						-1   ) ,						range(__lowerCamelCase ,						-1 ,						-1   )   ):
												if board[i][j] == 1:
																		return False
						for i, j in zip(range(__lowerCamelCase ,						-1 ,						-1   ) ,						range(__lowerCamelCase ,						len(__lowerCamelCase   )   )   ):
												if board[i][j] == 1:
																		return False
						return True






def _lowerCAmelCase	(  __lowerCamelCase:list[list[int]] ,						__lowerCamelCase:int   ):

						'''simple docstring'''






						if row >= len(__lowerCamelCase   ):
												solution.append(__lowerCamelCase   )
												printboard(__lowerCamelCase   )
												print()
												return True
						for i in range(len(__lowerCamelCase   )   ):
												if is_safe(__lowerCamelCase ,						__lowerCamelCase ,						__lowerCamelCase   ):
																		__magic_name__            =     1
																		solve(__lowerCamelCase ,						row + 1   )
																		__magic_name__            =     0
						return False






def _lowerCAmelCase	(  __lowerCamelCase:list[list[int]]   ):

						'''simple docstring'''






						for i in range(len(__lowerCamelCase   )   ):
												for j in range(len(__lowerCamelCase   )   ):
																		if board[i][j] == 1:
																								print("Q" ,						end=" "   )
																		else:
																								print("." ,						end=" "   )
												print()


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


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



