




def 		lowercase__ (		__A:						list[list[int]]				,__A:						list[list[int]]					):





					'''simple docstring'''






					__magic_name__				:						Dict     				=				[]
					__magic_name__				:						Any     				=				len(__A					)
					for i in range(__A					):
										__magic_name__				:						int     				=				[]
										for j in range(__A					):
															__magic_name__				:						Tuple     				=				0
															for k in range(__A					):
																				__magic_name__				:						Tuple     				=				val + matrix_a[i][k] * matrix_b[k][j]
															list_a.append(__A					)
										matrix_c.append(__A					)
					return matrix_c







def 		lowercase__ (		__A:						int					):





					'''simple docstring'''






					return [[int(row == column					) for column in range(__A					)] for row in range(__A					)]







def 		lowercase__ (		__A:						int					):





					'''simple docstring'''






					if n <= 1:
										return n
					__magic_name__				:						List[Any]     				=				identity(2					)
					__magic_name__				:						Optional[int]     				=				[[1, 1], [1, 0]]
					__magic_name__				:						Dict     				=				n - 1
					while n > 0:
										if n % 2 == 1:
															__magic_name__				:						Any     				=				multiply(__A				,__A					)
										__magic_name__				:						Optional[Any]     				=				multiply(__A				,__A					)
										__magic_name__				:						str     				=				int(n / 2					)
					return res_matrix[0][0]







def 		lowercase__ (		__A:						int					):





					'''simple docstring'''






					if n <= 1:
										return n
					__magic_name__				:						Union[str, Any]     				=				0
					__magic_name__				:						Optional[int]     				=				1
					for _ in range(2				,n + 1					):
										__magic_name__				,     __magic_name__				:						Tuple     				=				fiba, fiba + fiba
					return fiba







def 		lowercase__ (		):





					'''simple docstring'''






					for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
										__magic_name__				:						str     				=				int(''''''.join(c for c in ordinal if c in '''0123456789'''					)					)  # 1000th --> 1000
										print(
										    F'''{ordinal} fibonacci number using matrix exponentiation is '''
										    F'''{nth_fibonacci_matrix(__A					)} and using bruteforce is '''
										    F'''{nth_fibonacci_bruteforce(__A					)}\n'''					)
					# from timeit import timeit
					# print(timeit("nth_fibonacci_matrix(1000000)",
					#              "from main import nth_fibonacci_matrix", number=5))
					# print(timeit("nth_fibonacci_bruteforce(1000000)",
					#              "from main import nth_fibonacci_bruteforce", number=5))
					# 2.3342058970001744
					# 57.256506615000035


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	main()









def 		lowercase__ (		__A:						int					):





					'''simple docstring'''






					if not isinstance(__A				,__A					):
										__magic_name__				:						Dict     				=				F'''Input value of [number={number}] must be an integer'''
										raise TypeError(__A					)
					if number < 0 or number % 2 == 1:
										return False
					__magic_name__				:						Any     				=				int(number**0.5					)
					return number == number_sqrt * (number_sqrt + 1)


if __name__ == "__main__":
	import doctest

	doctest.testmod()



