


import math







def     lowerCAmelCase_					( __lowerCamelCase     ):

							if 1 < number < 4:
														# 2 and 3 are primes
														return True
							elif number < 2 or number % 2 == 0 or number % 3 == 0:
														# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
														return False

							# All primes number are in format of 6k +/- 1
							for i in range(5							,     int(math.sqrt(__lowerCamelCase     ) + 1     )							,     6     ):
														if number % i == 0 or number % (i + 2) == 0:
																					return False
							return True







def     lowerCAmelCase_					( __lowerCamelCase = 1_0_0_0_1     ):

							try:
														__snake_case		:      Optional[int]										=       int(__lowerCamelCase     )
							except (TypeError, ValueError):
														raise TypeError("Parameter nth must be int or castable to int."     ) from None
							if nth <= 0:
														raise ValueError("Parameter nth must be greater than or equal to one."     )
							__snake_case		:      list[int]										=       []
							__snake_case		:      Any										=       2
							while len(__lowerCamelCase     ) < nth:
														if is_prime(__lowerCamelCase     ):
																					primes.append(__lowerCamelCase     )
																					num += 1
														else:
																					num += 1
							return primes[len(__lowerCamelCase     ) - 1]


if __name__ == "__main__":
			print(f'''{solution() = }''')





from __future__ import annotations

_snake_case					:		Union[str, Any]      =    []







def     lowerCAmelCase_					( __lowerCamelCase							,     __lowerCamelCase							,     __lowerCamelCase     ):
							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							,     __lowerCamelCase     ):
							if row >= len(__lowerCamelCase     ):
														solution.append(__lowerCamelCase     )
														printboard(__lowerCamelCase     )
														print()
														return True
							for i in range(len(__lowerCamelCase     )     ):
														if is_safe(__lowerCamelCase							,     __lowerCamelCase							,     __lowerCamelCase     ):
																					__snake_case		:      Optional[Any]										=       1
																					solve(__lowerCamelCase							,     row + 1     )
																					__snake_case		:      Union[str, Any]										=       0
							return False







def     lowerCAmelCase_					( __lowerCamelCase     ):
							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"))
_snake_case					:		List[str]      =    8
_snake_case					:		Optional[int]      =    [[0 for i in range(n)] for j in range(n)]
solve(board, 0)

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

