
def 			UpperCamelCase       (				lowerCAmelCase__					,     lowerCAmelCase__						):
					'''simple docstring'''
					lowercase		      =		[]
					lowercase		      =		len(lowerCAmelCase__						)
					for i in range(lowerCAmelCase__						):
										lowercase		      =		[]
										for j in range(lowerCAmelCase__						):
															lowercase		      =		0
															for k in range(lowerCAmelCase__						):
																				lowercase		      =		val + matrix_a[i][k] * matrix_b[k][j]
															list_a.append(lowerCAmelCase__						)
										matrix_c.append(lowerCAmelCase__						)
					return matrix_c



def 			UpperCamelCase       (				lowerCAmelCase__						):
					'''simple docstring'''
					return [[int(row == column						) for column in range(lowerCAmelCase__						)] for row in range(lowerCAmelCase__						)]



def 			UpperCamelCase       (				lowerCAmelCase__						):
					'''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(lowerCAmelCase__					,     lowerCAmelCase__						)
										lowercase		      =		multiply(lowerCAmelCase__					,     lowerCAmelCase__						)
										lowercase		      =		int(n / 2						)
					return res_matrix[0][0]



def 			UpperCamelCase       (				lowerCAmelCase__						):
					'''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(lowerCAmelCase__						)} and using bruteforce is '
										    f'{nth_fibonacci_bruteforce(lowerCAmelCase__						)}\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()






import torch

from accelerate import Accelerator, DistributedType







class 							lowercase						:




							def __enter__(							self):
												if self.enabled:
																	lowercase		      =		self.model.no_sync()
																	self.model_sync_obj.__enter__()

												return self




							def __exit__(							self  ,A__  ,A__  ,A__):
												if self.enabled:
																	# Average all models on exit
																	self._sync_and_avg_model_params()
																	self.model_sync_obj.__exit__(A__  ,A__  ,A__)




							def __init__(							self  ,A__  ,A__  ,A__  ,A__ = True):
												if accelerator.distributed_type not in [
												    DistributedType.NO,
												    DistributedType.MULTI_CPU,
												    DistributedType.MULTI_GPU,
												]:
																	raise NotImplementedError('''LocalSGD is supported only for CPUs and GPUs (no DeepSpeed or MegatronLM)''')
												lowercase		      =		enabled and accelerator.distributed_type != DistributedType.NO
												lowercase		      =		0
												if self.enabled:
																	lowercase		      =		accelerator
																	lowercase		      =		model
																	lowercase		      =		local_sgd_steps




							def 					A__ (							self):
												self.num_steps += 1
												if not self.enabled:
																	return

												if self.num_steps % self.local_sgd_steps == 0:
																	self._sync_and_avg_model_params()





							def 					A__ (							self):
												self.accelerator.wait_for_everyone()
												with self.accelerator.autocast():
																	for param in self.model.parameters():
																						lowercase		      =		self.accelerator.reduce(param.data  ,reduction='''mean''')




