






import argparse
import os

import evaluate
import torch
from datasets import load_dataset
from torch.optim import AdamW
from torch.utils.data import DataLoader
from transformers import AutoModelForSequenceClassification, AutoTokenizer, get_linear_schedule_with_warmup, set_seed

from accelerate import Accelerator, DistributedType


########################################################################
# This is a fully working simple example to use Accelerate
# and perform gradient accumulation
#
# This example trains a Bert base model on GLUE MRPC
# in any of the following settings (with the same script):
#   - single CPU or single GPU
#   - multi GPUS (using PyTorch distributed mode)
#   - (multi) TPUs
#   - fp16 (mixed-precision) or fp32 (normal precision)
#
# To run it in each of these various modes, follow the instructions
# in the readme for examples:
# https://github.com/huggingface/accelerate/tree/main/examples
#
########################################################################


A__			:    int         =				16
A__			:    int         =				32






def 						a    (		lowerCamelCase_	,     lowerCamelCase_ = 16       ):






				'''simple docstring'''
				lowercase__     				=    AutoTokenizer.from_pretrained('''bert-base-cased'''       )
				lowercase__     				=    load_dataset('''glue'''	,     '''mrpc'''       )

				def tokenize_function(lowerCamelCase_       ):
								# max_length=None => use the model max length (it's actually the default)
								lowercase__     				=    tokenizer(examples['''sentence1''']	,     examples['''sentence2''']	,     truncation=lowerCamelCase_	,     max_length=lowerCamelCase_       )
								return outputs

				# Apply the method we just defined to all the examples in all the splits of the dataset
				# starting with the main process first:
				with accelerator.main_process_first():
								lowercase__     				=    datasets.map(
								    lowerCamelCase_	,     batched=lowerCamelCase_	,     remove_columns=['''idx''', '''sentence1''', '''sentence2''']	,     )

				# We also rename the 'label' column to 'labels' which is the expected name for labels by the models of the
				# transformers library
				lowercase__     				=    tokenized_datasets.rename_column('''label'''	,     '''labels'''       )

				def collate_fn(lowerCamelCase_       ):
								# On TPU it's best to pad everything to the same length or training will be very slow.
								lowercase__     				=    128 if accelerator.distributed_type == DistributedType.TPU else None
								# When using mixed precision we want round multiples of 8/16
								if accelerator.mixed_precision == "fp8":
												lowercase__     				=    16
								elif accelerator.mixed_precision != "no":
												lowercase__     				=    8
								else:
												lowercase__     				=    None

								return tokenizer.pad(
								    lowerCamelCase_	,     padding='''longest'''	,     max_length=lowerCamelCase_	,     pad_to_multiple_of=lowerCamelCase_	,     return_tensors='''pt'''	,     )

				# Instantiate dataloaders.
				lowercase__     				=    DataLoader(
				    tokenized_datasets['''train''']	,     shuffle=lowerCamelCase_	,     collate_fn=lowerCamelCase_	,     batch_size=lowerCamelCase_       )
				lowercase__     				=    DataLoader(
				    tokenized_datasets['''validation''']	,     shuffle=lowerCamelCase_	,     collate_fn=lowerCamelCase_	,     batch_size=lowerCamelCase_       )

				return train_dataloader, eval_dataloader


# For testing only
if os.environ.get('TESTING_MOCKED_DATALOADERS', None) == "1":
						from accelerate.test_utils.training import mocked_dataloaders

						A__			:    Dict         =				mocked_dataloaders  # noqa: F811






def 						a    (		lowerCamelCase_	,     lowerCamelCase_       ):






				'''simple docstring'''
				# For testing only
				if os.environ.get('''TESTING_MOCKED_DATALOADERS'''	,     lowerCamelCase_       ) == "1":
								lowercase__     				=    2
				# New Code #
				lowercase__     				=    int(args.gradient_accumulation_steps       )
				# Initialize accelerator
				lowercase__     				=    Accelerator(
				    cpu=args.cpu	,     mixed_precision=args.mixed_precision	,     gradient_accumulation_steps=lowerCamelCase_       )
				if accelerator.distributed_type == DistributedType.TPU and gradient_accumulation_steps > 1:
								raise NotImplementedError(
								    '''Gradient accumulation on TPUs is currently not supported. Pass `gradient_accumulation_steps=1`'''       )
				# Sample hyper-parameters for learning rate, batch size, seed and a few other HPs
				lowercase__     				=    config['''lr''']
				lowercase__     				=    int(config['''num_epochs''']       )
				lowercase__     				=    int(config['''seed''']       )
				lowercase__     				=    int(config['''batch_size''']       )

				lowercase__     				=    evaluate.load('''glue'''	,     '''mrpc'''       )

				set_seed(lowerCamelCase_       )
				lowercase__				,		lowercase__     				=    get_dataloaders(lowerCamelCase_	,     lowerCamelCase_       )
				# Instantiate the model (we build the model here so that the seed also control new weights initialization)
				lowercase__     				=    AutoModelForSequenceClassification.from_pretrained('''bert-base-cased'''	,     return_dict=lowerCamelCase_       )

				# We could avoid this line since the accelerator is set with `device_placement=True` (default value).
				# Note that if you are placing tensors on devices manually, this line absolutely needs to be before the optimizer
				# creation otherwise training will not work on TPU (`accelerate` will kindly throw an error to make us aware of that).
				lowercase__     				=    model.to(accelerator.device       )

				# Instantiate optimizer
				lowercase__     				=    AdamW(params=model.parameters()	,     lr=lowerCamelCase_       )

				# Instantiate scheduler
				lowercase__     				=    get_linear_schedule_with_warmup(
				    optimizer=lowerCamelCase_	,     num_warmup_steps=100	,     num_training_steps=(len(lowerCamelCase_       ) * num_epochs)	,     )

				# Prepare everything
				# There is no specific order to remember, we just need to unpack the objects in the same order we gave them to the
				# prepare method.
				lowercase__				,		lowercase__				,		lowercase__				,		lowercase__				,		lowercase__     				=    accelerator.prepare(
				    lowerCamelCase_	,     lowerCamelCase_	,     lowerCamelCase_	,     lowerCamelCase_	,     lowerCamelCase_       )

				# Now we train the model
				for epoch in range(lowerCamelCase_       ):
								model.train()
								for step, batch in enumerate(lowerCamelCase_       ):
												# We could avoid this line since we set the accelerator with `device_placement=True`.
												batch.to(accelerator.device       )
												# New code #
												# We use the new `accumulate` context manager to perform gradient accumulation
												# We also currently do not support TPUs nor advise it as bugs were found on the XLA side when running our tests.
												with accelerator.accumulate(lowerCamelCase_       ):
																lowercase__     				=    model(**lowerCamelCase_       )
																lowercase__     				=    output.loss
																accelerator.backward(lowerCamelCase_       )
																optimizer.step()
																lr_scheduler.step()
																optimizer.zero_grad()

								model.eval()
								for step, batch in enumerate(lowerCamelCase_       ):
												# We could avoid this line since we set the accelerator with `device_placement=True`.
												batch.to(accelerator.device       )
												with torch.no_grad():
																lowercase__     				=    model(**lowerCamelCase_       )
												lowercase__     				=    outputs.logits.argmax(dim=-1       )
												lowercase__				,		lowercase__     				=    accelerator.gather_for_metrics((predictions, batch['''labels'''])       )
												metric.add_batch(
												    predictions=lowerCamelCase_	,     references=lowerCamelCase_	,     )

								lowercase__     				=    metric.compute()
								# Use accelerator.print to print only on the main process.
								accelerator.print(F"""epoch {epoch}:"""	,     lowerCamelCase_       )






def 						a    (		):






				'''simple docstring'''
				lowercase__     				=    argparse.ArgumentParser(description='''Simple example of training script.'''       )
				parser.add_argument(
				    '''--mixed_precision'''	,     type=lowerCamelCase_	,     default=lowerCamelCase_	,     choices=['''no''', '''fp16''', '''bf16''', '''fp8''']	,     help='''Whether to use mixed precision. Choose'''
				    '''between fp16 and bf16 (bfloat16). Bf16 requires PyTorch >= 1.10.'''
				    '''and an Nvidia Ampere GPU.'''	,     )
				# New Code #
				parser.add_argument(
				    '''--gradient_accumulation_steps'''	,     type=lowerCamelCase_	,     default=1	,     help='''The number of minibatches to be ran before gradients are accumulated.'''	,     )
				parser.add_argument('''--cpu'''	,     action='''store_true'''	,     help='''If passed, will train on the CPU.'''       )
				lowercase__     				=    parser.parse_args()
				lowercase__     				=    {'''lr''': 2e-5, '''num_epochs''': 3, '''seed''': 42, '''batch_size''': 16}
				training_function(lowerCamelCase_	,     lowerCamelCase_       )


if __name__ == "__main__":
						main()












from math import sqrt






def 						a    (		lowerCamelCase_       ):






				'''simple docstring'''
				assert isinstance(lowerCamelCase_	,     lowerCamelCase_       ) and (
				    number >= 0
				), "'number' must been an int and positive"

				lowercase__     				=    True

				# 0 and 1 are none primes.
				if number <= 1:
								lowercase__     				=    False

				for divisor in range(2	,     int(round(sqrt(lowerCamelCase_       )       )       ) + 1       ):
								# if 'number' divisible by 'divisor' then sets 'status'
								# of false and break up the loop.
								if number % divisor == 0:
												lowercase__     				=    False
												break

    # precondition
				assert isinstance(lowerCamelCase_	,     lowerCamelCase_       ), "'status' must been from type bool"

				return status






def 						a    (		lowerCamelCase_       ):






				'''simple docstring'''
				assert isinstance(lowerCamelCase_	,     lowerCamelCase_       ) and (n > 2), "'N' must been an int and > 2"

				# beginList: contains all natural numbers from 2 up to N
				lowercase__     				=    list(range(2	,     n + 1       )       )

				lowercase__     				=    []  # this list will be returns.

				# actual sieve of erathostenes
				for i in range(len(lowerCamelCase_       )       ):
								for j in range(i + 1	,     len(lowerCamelCase_       )       ):
												if (begin_list[i] != 0) and (begin_list[j] % begin_list[i] == 0):
																lowercase__     				=    0

    # filters actual prime numbers.
				lowercase__     				=    [x for x in begin_list if x != 0]

				# precondition
				assert isinstance(lowerCamelCase_	,     lowerCamelCase_       ), "'ans' must been from type list"

				return ans






def 						a    (		lowerCamelCase_       ):






				'''simple docstring'''
				assert isinstance(lowerCamelCase_	,     lowerCamelCase_       ) and (n > 2), "'N' must been an int and > 2"

				lowercase__     				=    []

				# iterates over all numbers between 2 up to N+1
				# if a number is prime then appends to list 'ans'
				for number in range(2	,     n + 1       ):
								if is_prime(lowerCamelCase_       ):
												ans.append(lowerCamelCase_       )

    # precondition
				assert isinstance(lowerCamelCase_	,     lowerCamelCase_       ), "'ans' must been from type list"

				return ans






def 						a    (		lowerCamelCase_       ):






				'''simple docstring'''
				assert isinstance(lowerCamelCase_	,     lowerCamelCase_       ) and number >= 0, "'number' must been an int and >= 0"

				lowercase__     				=    []  # this list will be returns of the function.

				# potential prime number factors.

				lowercase__     				=    2

				lowercase__     				=    number

				if number == 0 or number == 1:
								ans.append(lowerCamelCase_       )

				# if 'number' not prime then builds the prime factorization of 'number'
				elif not is_prime(lowerCamelCase_       ):
								while quotient != 1:
												if is_prime(lowerCamelCase_       ) and (quotient % factor == 0):
																ans.append(lowerCamelCase_       )
																quotient /= factor
												else:
																factor += 1

				else:
								ans.append(lowerCamelCase_       )

				# precondition
				assert isinstance(lowerCamelCase_	,     lowerCamelCase_       ), "'ans' must been from type list"

				return ans






def 						a    (		lowerCamelCase_       ):






				'''simple docstring'''
				assert isinstance(lowerCamelCase_	,     lowerCamelCase_       ) and (
				    number >= 0
				), "'number' bust been an int and >= 0"

				lowercase__     				=    0

				# prime factorization of 'number'
				lowercase__     				=    prime_factorization(lowerCamelCase_       )

				lowercase__     				=    max(lowerCamelCase_       )

				# precondition
				assert isinstance(lowerCamelCase_	,     lowerCamelCase_       ), "'ans' must been from type int"

				return ans






def 						a    (		lowerCamelCase_       ):






				'''simple docstring'''
				assert isinstance(lowerCamelCase_	,     lowerCamelCase_       ) and (
				    number >= 0
				), "'number' bust been an int and >= 0"

				lowercase__     				=    0

				# prime factorization of 'number'
				lowercase__     				=    prime_factorization(lowerCamelCase_       )

				lowercase__     				=    min(lowerCamelCase_       )

				# precondition
				assert isinstance(lowerCamelCase_	,     lowerCamelCase_       ), "'ans' must been from type int"

				return ans






def 						a    (		lowerCamelCase_       ):






				'''simple docstring'''
				assert isinstance(lowerCamelCase_	,     lowerCamelCase_       ), "'number' must been an int"
				assert isinstance(number % 2 == 0	,     lowerCamelCase_       ), "compare bust been from type bool"

				return number % 2 == 0






def 						a    (		lowerCamelCase_       ):






				'''simple docstring'''
				assert isinstance(lowerCamelCase_	,     lowerCamelCase_       ), "'number' must been an int"
				assert isinstance(number % 2 != 0	,     lowerCamelCase_       ), "compare bust been from type bool"

				return number % 2 != 0






def 						a    (		lowerCamelCase_       ):






				'''simple docstring'''
				assert (
				    isinstance(lowerCamelCase_	,     lowerCamelCase_       ) and (number > 2) and is_even(lowerCamelCase_       )
				), "'number' must been an int, even and > 2"

				lowercase__     				=    []  # this list will returned

				# creates a list of prime numbers between 2 up to 'number'
				lowercase__     				=    get_prime_numbers(lowerCamelCase_       )
				lowercase__     				=    len(lowerCamelCase_       )

				# run variable for while-loops.
				lowercase__     				=    0
				lowercase__     				=    None

				# exit variable. for break up the loops
				lowercase__     				=    True

				while i < len_pn and loop:
								lowercase__     				=    i + 1

								while j < len_pn and loop:
												if prime_numbers[i] + prime_numbers[j] == number:
																lowercase__     				=    False
																ans.append(prime_numbers[i]       )
																ans.append(prime_numbers[j]       )

												j += 1

								i += 1

				# precondition
				assert (
				    isinstance(lowerCamelCase_	,     lowerCamelCase_       )
				    and (len(lowerCamelCase_       ) == 2)
				    and (ans[0] + ans[1] == number)
				    and is_prime(ans[0]       )
				    and is_prime(ans[1]       )
				), "'ans' must contains two primes. And sum of elements must been eq 'number'"

				return ans






def 						a    (		lowerCamelCase_	,     lowerCamelCase_       ):






				'''simple docstring'''
				assert (
				    isinstance(lowerCamelCase_	,     lowerCamelCase_       )
				    and isinstance(lowerCamelCase_	,     lowerCamelCase_       )
				    and (numbera >= 0)
				    and (numbera >= 0)
				), "'number1' and 'number2' must been positive integer."

				lowercase__     				=    0

				while numbera != 0:
								lowercase__     				=    numbera % numbera
								lowercase__     				=    numbera
								lowercase__     				=    rest

				# precondition
				assert isinstance(lowerCamelCase_	,     lowerCamelCase_       ) and (
				    numbera >= 0
				), "'number' must been from type int and positive"

				return numbera






def 						a    (		lowerCamelCase_	,     lowerCamelCase_       ):






				'''simple docstring'''
				assert (
				    isinstance(lowerCamelCase_	,     lowerCamelCase_       )
				    and isinstance(lowerCamelCase_	,     lowerCamelCase_       )
				    and (numbera >= 1)
				    and (numbera >= 1)
				), "'number1' and 'number2' must been positive integer."

				lowercase__     				=    1  # actual answer that will be return.

				# for kgV (x,1)
				if numbera > 1 and numbera > 1:
								# builds the prime factorization of 'number1' and 'number2'
								lowercase__     				=    prime_factorization(lowerCamelCase_       )
								lowercase__     				=    prime_factorization(lowerCamelCase_       )

				elif numbera == 1 or numbera == 1:
								lowercase__     				=    []
								lowercase__     				=    []
								lowercase__     				=    max(lowerCamelCase_	,     lowerCamelCase_       )

				lowercase__     				=    0
				lowercase__     				=    0

				lowercase__     				=    []  # captured numbers int both 'primeFac1' and 'primeFac2'

				# iterates through primeFac1
				for n in prime_fac_a:
								if n not in done:
												if n in prime_fac_a:
																lowercase__     				=    prime_fac_a.count(lowerCamelCase_       )
																lowercase__     				=    prime_fac_a.count(lowerCamelCase_       )

																for _ in range(max(lowerCamelCase_	,     lowerCamelCase_       )       ):
																				ans *= n

												else:
																lowercase__     				=    prime_fac_a.count(lowerCamelCase_       )

																for _ in range(lowerCamelCase_       ):
																				ans *= n

												done.append(lowerCamelCase_       )

    # iterates through primeFac2
				for n in prime_fac_a:
								if n not in done:
												lowercase__     				=    prime_fac_a.count(lowerCamelCase_       )

												for _ in range(lowerCamelCase_       ):
																ans *= n

												done.append(lowerCamelCase_       )

    # precondition
				assert isinstance(lowerCamelCase_	,     lowerCamelCase_       ) and (
				    ans >= 0
				), "'ans' must been from type int and positive"

				return ans






def 						a    (		lowerCamelCase_       ):






				'''simple docstring'''
				assert isinstance(lowerCamelCase_	,     lowerCamelCase_       ) and (n >= 0), "'number' must been a positive int"

				lowercase__     				=    0
				lowercase__     				=    2  # this variable holds the answer

				while index < n:
								index += 1

								ans += 1  # counts to the next number

								# if ans not prime then
								# runs to the next prime number.
								while not is_prime(lowerCamelCase_       ):
												ans += 1

    # precondition
				assert isinstance(lowerCamelCase_	,     lowerCamelCase_       ) and is_prime(
				    lowerCamelCase_       ), "'ans' must been a prime number and from type int"

				return ans






def 						a    (		lowerCamelCase_	,     lowerCamelCase_       ):






				'''simple docstring'''
				assert (
				    is_prime(lowerCamelCase_       ) and is_prime(lowerCamelCase_       ) and (p_number_a < p_number_a)
				), "The arguments must been prime numbers and 'pNumber1' < 'pNumber2'"

				lowercase__     				=    p_number_a + 1  # jump to the next number

				lowercase__     				=    []  # this list will be returns.

				# if number is not prime then
				# fetch the next prime number.
				while not is_prime(lowerCamelCase_       ):
								number += 1

				while number < p_number_a:
								ans.append(lowerCamelCase_       )

								number += 1

								# fetch the next prime number.
								while not is_prime(lowerCamelCase_       ):
												number += 1

    # precondition
				assert (
				    isinstance(lowerCamelCase_	,     lowerCamelCase_       )
				    and ans[0] != p_number_a
				    and ans[len(lowerCamelCase_       ) - 1] != p_number_a
				), "'ans' must been a list without the arguments"

				# 'ans' contains not 'pNumber1' and 'pNumber2' !
				return ans






def 						a    (		lowerCamelCase_       ):






				'''simple docstring'''
				assert isinstance(lowerCamelCase_	,     lowerCamelCase_       ) and (n >= 1), "'n' must been int and >= 1"

				lowercase__     				=    []  # will be returned.

				for divisor in range(1	,     n + 1       ):
								if n % divisor == 0:
												ans.append(lowerCamelCase_       )

    # precondition
				assert ans[0] == 1 and ans[len(lowerCamelCase_       ) - 1] == n, "Error in function getDivisiors(...)"

				return ans






def 						a    (		lowerCamelCase_       ):






				'''simple docstring'''
				assert isinstance(lowerCamelCase_	,     lowerCamelCase_       ) and (
				    number > 1
				), "'number' must been an int and >= 1"

				lowercase__     				=    get_divisors(lowerCamelCase_       )

				# precondition
				assert (
				    isinstance(lowerCamelCase_	,     lowerCamelCase_       )
				    and (divisors[0] == 1)
				    and (divisors[len(lowerCamelCase_       ) - 1] == number)
				), "Error in help-function getDivisiors(...)"

				# summed all divisors up to 'number' (exclusive), hence [:-1]
				return sum(divisors[:-1]       ) == number






def 						a    (		lowerCamelCase_	,     lowerCamelCase_       ):






				'''simple docstring'''
				assert (
				    isinstance(lowerCamelCase_	,     lowerCamelCase_       )
				    and isinstance(lowerCamelCase_	,     lowerCamelCase_       )
				    and (denominator != 0)
				), "The arguments must been from type int and 'denominator' != 0"

				# build the greatest common divisor of numerator and denominator.
				lowercase__     				=    gcd(abs(lowerCamelCase_       )	,     abs(lowerCamelCase_       )       )

				# precondition
				assert (
				    isinstance(lowerCamelCase_	,     lowerCamelCase_       )
				    and (numerator % gcd_of_fraction == 0)
				    and (denominator % gcd_of_fraction == 0)
				), "Error in function gcd(...,...)"

				return (numerator // gcd_of_fraction, denominator // gcd_of_fraction)






def 						a    (		lowerCamelCase_       ):






				'''simple docstring'''
				assert isinstance(lowerCamelCase_	,     lowerCamelCase_       ) and (n >= 0), "'n' must been a int and >= 0"

				lowercase__     				=    1  # this will be return.

				for factor in range(1	,     n + 1       ):
								ans *= factor

				return ans






def 						a    (		lowerCamelCase_       ):






				'''simple docstring'''
				assert isinstance(lowerCamelCase_	,     lowerCamelCase_       ) and (n >= 0), "'n' must been an int and >= 0"

				lowercase__     				=    0
				lowercase__     				=    1
				lowercase__     				=    1  # this will be return

				for _ in range(n - 1       ):
								lowercase__     				=    ans
								ans += fiba
								lowercase__     				=    tmp

				return ans




