



def 	a						(				_UpperCAmelCase							: list[list[int]]			,       _UpperCAmelCase							: list[list[int]]						):







		'''simple docstring'''





		__UpperCAmelCase   :					Tuple													=     []
		__UpperCAmelCase   :					str													=     len(_UpperCAmelCase						)
		for i in range(_UpperCAmelCase						):
				__UpperCAmelCase   :					int													=     []
				for j in range(_UpperCAmelCase						):
						__UpperCAmelCase   :					Optional[Any]													=     0
						for k in range(_UpperCAmelCase						):
								__UpperCAmelCase   :					Optional[int]													=     val + matrix_a[i][k] * matrix_b[k][j]
						list_a.append(_UpperCAmelCase						)
				matrix_c.append(_UpperCAmelCase						)
		return matrix_c

def 	a						(				_UpperCAmelCase							: int						):







		'''simple docstring'''





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

def 	a						(				_UpperCAmelCase							: int						):







		'''simple docstring'''





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

def 	a						(				_UpperCAmelCase							: int						):







		'''simple docstring'''





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

def 	a						(				):







		'''simple docstring'''





		for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
				__UpperCAmelCase   :					Optional[Any]													=     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(_UpperCAmelCase						)} and using bruteforce is '
				    f'{nth_fibonacci_bruteforce(_UpperCAmelCase						)}\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 	a						(				_UpperCAmelCase							: str						):







		'''simple docstring'''





		__UpperCAmelCase   :					Optional[Any]													=     53_81
		for x in s:
				__UpperCAmelCase   :					str													=     ((hash_value << 5) + hash_value) + ord(_UpperCAmelCase						)
		return hash_value & 0xFFFF_FFFF





