






'''simple docstring'''







from __future__ import annotations

import math





def 		_UpperCAmelCase   (							__A							:   float						,		__A							:   int      ):
				a_		:  Any											=      u
				for i in range(1						,		__A      ):
								a_		:  int											=      temp * (u - i)
				return temp





def 		_UpperCAmelCase   (							):
				a_		:  Tuple											=      int(input('''enter the numbers of values: '''      )      )
				a_		:  list[list[float]]											=      []
				for _ in range(__A      ):
								y.append([]      )
				for i in range(__A      ):
								for j in range(__A      ):
												y[i].append(__A      )
												a_		:  List[str]											=      0

				print('''enter the values of parameters in a list: '''      )
				a_		:  List[Any]											=      list(map(__A						,		input().split()      )      )

				print('''enter the values of corresponding parameters: '''      )
				for i in range(__A      ):
								a_		:  Optional[Any]											=      float(input()      )

				a_		:  Union[str, Any]											=      int(input('''enter the value to interpolate: '''      )      )
				a_		:  Any											=      (value - x[0]) / (x[1] - x[0])

				# for calculating forward difference table

				for i in range(1						,		__A      ):
								for j in range(n - i      ):
												a_		:  Optional[Any]											=      y[j + 1][i - 1] - y[j][i - 1]

				a_		:  Optional[int]											=      y[0][0]
				for i in range(1						,		__A      ):
								summ += (ucal(__A						,		__A      ) * y[0][i]) / math.factorial(__A      )

				print(f'the value at {value} is {summ}'      )


if __name__ == "__main__":
		main()












'''simple docstring'''







from __future__ import annotations





def 		_UpperCAmelCase   (							__A							:   tuple[int, int]						,		__A							:   int      ):
				a_				,			a_		:  List[str]											=      position
				a_		:  Optional[int]											=      [
				    (y + 1, x + 2),
				    (y - 1, x + 2),
				    (y + 1, x - 2),
				    (y - 1, x - 2),
				    (y + 2, x + 1),
				    (y + 2, x - 1),
				    (y - 2, x + 1),
				    (y - 2, x - 1),
				]
				a_		:  Any											=      []

				for position in positions:
								a_				,			a_		:  Dict											=      position
								if 0 <= y_test < n and 0 <= x_test < n:
												permissible_positions.append(__A      )

				return permissible_positions





def 		_UpperCAmelCase   (							__A							:   list[list[int]]      ):
				return not any(elem == 0 for row in board for elem in row      )





def 		_UpperCAmelCase   (							__A							:   list[list[int]]						,		__A							:   tuple[int, int]						,		__A							:   int      ):

				if is_complete(__A      ):
								return True

				for position in get_valid_pos(__A						,		len(__A      )      ):
								a_				,			a_		:  Dict											=      position

								if board[y][x] == 0:
												a_		:  Optional[Any]											=      curr + 1
												if open_knight_tour_helper(__A						,		__A						,		curr + 1      ):
																return True
												a_		:  Tuple											=      0

				return False





def 		_UpperCAmelCase   (							__A							:   int      ):
				a_		:  List[str]											=      [[0 for i in range(__A      )] for j in range(__A      )]

				for i in range(__A      ):
								for j in range(__A      ):
												a_		:  Optional[Any]											=      1
												if open_knight_tour_helper(__A						,		(i, j)						,		1      ):
																return board
												a_		:  Union[str, Any]											=      0

				a_		:  Dict											=      f'Open Kight Tour cannot be performed on a board of size {n}'
				raise ValueError(__A      )


if __name__ == "__main__":
		import doctest

		doctest.testmod()




