






"""simple docstring"""



from collections.abc import Callable

import numpy as np




def      _lowerCAmelCase		(							UpperCAmelCase__       :					Callable,						UpperCAmelCase__       :					float,						UpperCAmelCase__       :					float,						UpperCAmelCase__       :					float,						UpperCAmelCase__       :					float      )		->np.array:
						A__						:  Dict		  =  int(np.ceil((x_end - xa) / step_size      )      )
						A__						:  Any		  =  np.zeros((n + 1,)      )
						A__						:  Tuple		  =  ya
						A__						:  List[Any]		  =  xa

						for k in range(UpperCAmelCase__      ):
												A__						:  List[str]		  =  y[k] + step_size * ode_func(UpperCAmelCase__,						y[k]      )
												A__						:  str		  =  y[k] + (
												    (step_size / 2) * (ode_func(UpperCAmelCase__,						y[k]      ) + ode_func(x + step_size,						UpperCAmelCase__      ))
												)
												x += step_size

						return y


if __name__ == "__main__":
						import doctest

						doctest.testmod()














"""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))






