






def 	_UpperCAmelCase    (  a		:	int							)			->			bool:





						"""simple docstring"""

						if p < 2:
												raise ValueError('p should not be less than 2!'							)
						elif p == 2:
												return True

						lowercase_      :   str        =			4
						lowercase_      :   Union[str, Any]        =			(1 << p) - 1
						for _ in range(p - 2							):
												lowercase_      :   Optional[int]        =			((s * s) - 2) % m
						return s == 0


if __name__ == "__main__":
						print(lucas_lehmer_test(7))
						print(lucas_lehmer_test(1_1))








'''simple docstring'''

from __future__ import annotations






def 	_UpperCAmelCase    (  a		:	int = 4							)			->			list[list[int]]:





						"""simple docstring"""
						lowercase_      :   Tuple        =			abs(a							) or 4
						return [[1 + x + y * row_size for x in range(a							)] for y in range(a							)]






def 	_UpperCAmelCase    (  a		:	list[list[int]]							)			->			list[list[int]]:





						"""simple docstring"""
						return reverse_row(transpose(a							)							)
						# OR.. transpose(reverse_column(matrix))






def 	_UpperCAmelCase    (  a		:	list[list[int]]							)			->			list[list[int]]:





						"""simple docstring"""
						return reverse_row(reverse_column(a							)							)
						# OR.. reverse_column(reverse_row(matrix))






def 	_UpperCAmelCase    (  a		:	list[list[int]]							)			->			list[list[int]]:





						"""simple docstring"""
						return reverse_column(transpose(a							)							)
						# OR.. transpose(reverse_row(matrix))






def 	_UpperCAmelCase    (  a		:	list[list[int]]							)			->			list[list[int]]:





						"""simple docstring"""
						lowercase_      :   Any        =			[list(a							) for x in zip(*a							)]
						return matrix






def 	_UpperCAmelCase    (  a		:	list[list[int]]							)			->			list[list[int]]:





						"""simple docstring"""
						lowercase_      :   List[str]        =			matrix[::-1]
						return matrix






def 	_UpperCAmelCase    (  a		:	list[list[int]]							)			->			list[list[int]]:





						"""simple docstring"""
						lowercase_      :   str        =			[x[::-1] for x in matrix]
						return matrix






def 	_UpperCAmelCase    (  a		:	list[list[int]]							)			->			None:





						"""simple docstring"""
						for i in matrix:
												print(*a							)


if __name__ == "__main__":
						A:      Dict  				=				make_matrix()
						print("\norigin:\n")
						print_matrix(matrix)
						print("\nrotate 90 counterclockwise:\n")
						print_matrix(rotate_aa(matrix))

						A:      List[Any]  				=				make_matrix()
						print("\norigin:\n")
						print_matrix(matrix)
						print("\nrotate 180:\n")
						print_matrix(rotate_aaa(matrix))

						A:      List[str]  				=				make_matrix()
						print("\norigin:\n")
						print_matrix(matrix)
						print("\nrotate 270 counterclockwise:\n")
						print_matrix(rotate_aaa(matrix))
