




'''simple docstring'''
import unittest
from functools import partial

import torch

from accelerate import Accelerator, debug_launcher
from accelerate.state import AcceleratorState, GradientState
from accelerate.test_utils import require_cpu, require_huggingface_suite
from accelerate.utils import GradientAccumulationPlugin
def 							snake_case_    (  a__						:      Dict=2       ,a__						:      List[Any]=True       ,a__						:      int=False     ):



    """simple docstring"""




    __lowercase     							=		Accelerator(step_scheduler_with_optimizer=a__       ,split_batches=a__     )
    __lowercase     							=		torch.nn.Linear(2       ,4     )
    __lowercase     							=		torch.optim.AdamW(model.parameters()       ,lr=1.0     )
    __lowercase     							=		torch.optim.lr_scheduler.OneCycleLR(a__       ,max_lr=0.0_1       ,steps_per_epoch=2       ,epochs=1     )
    __lowercase							,__lowercase							,__lowercase     							=		accelerator.prepare(a__       ,a__       ,a__     )

    # Optimizer has stepped
    scheduler.step()
    if step_scheduler_with_optimizer or (num_processes == 1):
        assert (
            scheduler.scheduler.last_epoch == num_processes
        ), f'Last Epoch ({scheduler.scheduler.last_epoch}) != Num Processes ({num_processes})'
    else:
        assert (
            scheduler.scheduler.last_epoch != num_processes
        ), f'Last Epoch ({scheduler.scheduler.last_epoch}) == Num Processes ({num_processes})'
def 							snake_case_    (  a__						:      Union[str, Any]=2       ,a__						:      Dict=True       ,a__						:      Any=False     ):



    """simple docstring"""




    __lowercase     							=		Accelerator(step_scheduler_with_optimizer=a__       ,split_batches=a__     )
    __lowercase     							=		torch.nn.Linear(2       ,4     )
    __lowercase     							=		torch.optim.AdamW(model.parameters()       ,lr=1.0     )
    __lowercase     							=		torch.optim.lr_scheduler.LambdaLR(a__       ,lr_lambda=lambda a__     : 1 - n / 10     )
    __lowercase							,__lowercase							,__lowercase     							=		accelerator.prepare(a__       ,a__       ,a__     )

    # Optimizer has stepped
    __lowercase     							=		False
    scheduler.step()
    __lowercase     							=		1 - (num_processes if (step_scheduler_with_optimizer and not split_batches) else 1) / 10
    assert (
        scheduler.get_last_lr()[0] == expected_lr
    ), f'Wrong lr found at first step, expected {expected_lr}, got {scheduler.get_last_lr()[0]}'

    # Optimizer has not stepped
    __lowercase     							=		True
    scheduler.step()
    if not step_scheduler_with_optimizer:
        __lowercase     							=		1 - 2 / 10
    assert (
        scheduler.get_last_lr()[0] == expected_lr
    ), f'Wrong lr found at second step, expected {expected_lr}, got {scheduler.get_last_lr()[0]}'
def 							snake_case_    (  a__						:      int = 2     ):



    """simple docstring"""




    from transformers import get_linear_schedule_with_warmup

    __lowercase     							=		[1, 2, 4]
    for num_steps in steps:
        __lowercase     							=		GradientAccumulationPlugin(num_steps=a__       ,adjust_scheduler=num_steps > 1     )
        __lowercase     							=		Accelerator(gradient_accumulation_plugin=a__     )
        __lowercase     							=		torch.nn.Linear(2       ,4     )
        __lowercase     							=		torch.optim.AdamW(model.parameters()       ,lr=1_0.0     )
        __lowercase     							=		get_linear_schedule_with_warmup(optimizer=a__       ,num_warmup_steps=0       ,num_training_steps=20     )

        __lowercase							,__lowercase							,__lowercase     							=		accelerator.prepare(a__       ,a__       ,a__     )

        for i in range(10 * num_steps     ):
            with accelerator.accumulate(a__     ):
                optimizer.step()
                scheduler.step()

            if i == (10 * num_steps - 2):
                assert (
                    scheduler.get_last_lr()[0] != 0
                ), f'Wrong lr found at second-to-last step, expected non-zero, got {scheduler.get_last_lr()[0]}. num_steps: {num_steps}'
        assert (
            scheduler.get_last_lr()[0] == 0
        ), f'Wrong lr found at last step, expected 0, got {scheduler.get_last_lr()[0]}'
        GradientState._reset_state()






@require_cpu
class 			SCREAMING_SNAKE_CASE(							unittest.TestCase	):

       def        snake_case__     (       self	)       ->   Tuple:

           """simple docstring"""



           debug_launcher(partial(lowerCamelCase__   ,						num_processes=1	)   ,						num_processes=1	)
           debug_launcher(partial(lowerCamelCase__   ,						num_processes=1   ,						split_batches=lowerCamelCase__	)   ,						num_processes=1	)

       def        snake_case__     (       self	)       ->   Tuple:

           """simple docstring"""



           debug_launcher(partial(lowerCamelCase__   ,						num_processes=1	)   ,						num_processes=1	)
           debug_launcher(partial(lowerCamelCase__   ,						num_processes=1   ,						split_batches=lowerCamelCase__	)   ,						num_processes=1	)

       def        snake_case__     (       self	)       ->   List[str]:

           """simple docstring"""



           debug_launcher(partial(lowerCamelCase__   ,						num_processes=1   ,						step_scheduler_with_optimizer=lowerCamelCase__	)   ,						num_processes=1	)

       def        snake_case__     (       self	)       ->   Any:

           """simple docstring"""



           debug_launcher(partial(lowerCamelCase__   ,						num_processes=1   ,						step_scheduler_with_optimizer=lowerCamelCase__	)   ,						num_processes=1	)

       def        snake_case__     (       self	)       ->   Optional[Any]:

           """simple docstring"""



           AcceleratorState._reset_state(lowerCamelCase__	)
           debug_launcher(lowerCamelCase__	)
           debug_launcher(partial(lowerCamelCase__   ,						num_processes=1   ,						split_batches=lowerCamelCase__	)   ,						num_processes=1	)

       def        snake_case__     (       self	)       ->   Union[str, Any]:

           """simple docstring"""



           AcceleratorState._reset_state(lowerCamelCase__	)
           debug_launcher(lowerCamelCase__	)
           debug_launcher(partial(lowerCamelCase__   ,						num_processes=1   ,						split_batches=lowerCamelCase__	)   ,						num_processes=1	)

       def        snake_case__     (       self	)       ->   Optional[Any]:

           """simple docstring"""



           AcceleratorState._reset_state(lowerCamelCase__	)
           debug_launcher(partial(lowerCamelCase__   ,						step_scheduler_with_optimizer=lowerCamelCase__	)	)

       def        snake_case__     (       self	)       ->   List[str]:

           """simple docstring"""



           AcceleratorState._reset_state(lowerCamelCase__	)
           debug_launcher(partial(lowerCamelCase__   ,						step_scheduler_with_optimizer=lowerCamelCase__	)	)




       @require_huggingface_suite
       def        snake_case__     (       self	)       ->   Dict:

           """simple docstring"""



           AcceleratorState._reset_state(lowerCamelCase__	)
           debug_launcher(partial(lowerCamelCase__   ,						num_processes=1	)	)
           debug_launcher(lowerCamelCase__	)










'''simple docstring'''
from math import gcd
def 							snake_case_    (  a__						:      int = 1_20_00     ):



    """simple docstring"""




    __lowercase     							=		0
    for d in range(max_d + 1     ):
        for n in range(d // 3 + 1       ,(d + 1) // 2     ):
            if gcd(a__       ,a__     ) == 1:
                fractions_number += 1
    return fractions_number


if __name__ == "__main__":
  print(F"""{solution() = }""")




