
def 						UpperCAmelCase      (     a_						)		->     list:







				"""simple docstring"""



				__A             =			int(a_						)
				if n_element < 1:
								__A             =			ValueError("a should be a positive number"						)
								raise my_error

				__A             =			[1]
				__A      ,							__A      ,							__A             =			(0, 0, 0)
				__A             =			1
				while index < n_element:
								while hamming_list[i] * 2 <= hamming_list[-1]:
												i += 1
								while hamming_list[j] * 3 <= hamming_list[-1]:
												j += 1
								while hamming_list[k] * 5 <= hamming_list[-1]:
												k += 1
								hamming_list.append(
								    min(hamming_list[i] * 2		,       hamming_list[j] * 3		,       hamming_list[k] * 5						)						)
								index += 1
				return hamming_list


if __name__ == "__main__":
					SCREAMING_SNAKE_CASE							:Optional[int]										=    input('Enter the last number (nth term) of the Hamming Number Series: ')
					print('Formula of Hamming Number Series => 2^i * 3^j * 5^k')
					SCREAMING_SNAKE_CASE							:int										=    hamming(int(n))
					print('-----------------------------------------------------')
					print(f'''The list with nth numbers is: {hamming_numbers}''')
					print('-----------------------------------------------------')


from __future__ import annotations


def 						UpperCAmelCase      (     a_ = 4						)		->     list[list[int]]:







				"""simple docstring"""



				__A             =			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]]:







				"""simple docstring"""



				return reverse_row(transpose(a_						)						)
				# OR.. transpose(reverse_column(matrix))


def 						UpperCAmelCase      (     a_						)		->     list[list[int]]:







				"""simple docstring"""



				return reverse_row(reverse_column(a_						)						)
				# OR.. reverse_column(reverse_row(matrix))


def 						UpperCAmelCase      (     a_						)		->     list[list[int]]:







				"""simple docstring"""



				return reverse_column(transpose(a_						)						)
				# OR.. transpose(reverse_row(matrix))


def 						UpperCAmelCase      (     a_						)		->     list[list[int]]:







				"""simple docstring"""



				__A             =			[list(a_						) for x in zip(*a_						)]
				return matrix


def 						UpperCAmelCase      (     a_						)		->     list[list[int]]:







				"""simple docstring"""



				__A             =			matrix[::-1]
				return matrix


def 						UpperCAmelCase      (     a_						)		->     list[list[int]]:







				"""simple docstring"""



				__A             =			[x[::-1] for x in matrix]
				return matrix


def 						UpperCAmelCase      (     a_						)		->     None:







				"""simple docstring"""



				for i in matrix:
								print(*a_						)


if __name__ == "__main__":
					SCREAMING_SNAKE_CASE							:Union[str, Any]										=    make_matrix()
					print('\norigin:\n')
					print_matrix(matrix)
					print('\nrotate 90 counterclockwise:\n')
					print_matrix(rotate_aa(matrix))

					SCREAMING_SNAKE_CASE							:Tuple										=    make_matrix()
					print('\norigin:\n')
					print_matrix(matrix)
					print('\nrotate 180:\n')
					print_matrix(rotate_aaa(matrix))

					SCREAMING_SNAKE_CASE							:Union[str, Any]										=    make_matrix()
					print('\norigin:\n')
					print_matrix(matrix)
					print('\nrotate 270 counterclockwise:\n')
					print_matrix(rotate_aaa(matrix))
