def     UpperCAmelCase						(   lowercase							,      lowercase							):







				"""simple docstring"""



				__lowercase			      =							[]
				__lowercase			      =							len(lowercase							)
				for i in range(lowercase							):
								__lowercase			      =							[]
								for j in range(lowercase							):
												__lowercase			      =							0
												for k in range(lowercase							):
																__lowercase			      =							val + matrix_a[i][k] * matrix_b[k][j]
												list_a.append(lowercase							)
								matrix_c.append(lowercase							)
				return matrix_c





def     UpperCAmelCase						(   lowercase							):







				"""simple docstring"""



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





def     UpperCAmelCase						(   lowercase							):







				"""simple docstring"""



				if n <= 1:
								return n
				__lowercase			      =							identity(2							)
				__lowercase			      =							[[1, 1], [1, 0]]
				__lowercase			      =							n - 1
				while n > 0:
								if n % 2 == 1:
												__lowercase			      =							multiply(lowercase							,      lowercase							)
								__lowercase			      =							multiply(lowercase							,      lowercase							)
								__lowercase			      =							int(n / 2							)
				return res_matrix[0][0]





def     UpperCAmelCase						(   lowercase							):







				"""simple docstring"""



				if n <= 1:
								return n
				__lowercase			      =							0
				__lowercase			      =							1
				for _ in range(2							,      n + 1							):
								__lowercase      ,					__lowercase			      =							fiba, fiba + fiba
				return fiba





def     UpperCAmelCase						(   ):







				"""simple docstring"""



				for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
								__lowercase			      =							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(lowercase							)} and using bruteforce is "
								    F"{nth_fibonacci_bruteforce(lowercase							)}\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()
from typing import TypeVar

from .arrow_dataset import Dataset, _split_by_node_map_style_dataset
from .iterable_dataset import IterableDataset, _split_by_node_iterable_dataset


__a  :					Union[str, Any]          =  TypeVar("""DatasetType""", Dataset, IterableDataset)





def     UpperCAmelCase						(   lowercase							,      lowercase							,      lowercase							):







				"""simple docstring"""



				if isinstance(lowercase							,      lowercase							):
								return _split_by_node_map_style_dataset(lowercase							,      rank=lowercase							,      world_size=lowercase							)
				else:
								return _split_by_node_iterable_dataset(lowercase							,      rank=lowercase							,      world_size=lowercase							)