

'''simple docstring'''
import inspect
import os

import torch
from transformers import AutoModel
from transformers.testing_utils import mockenv_context
from transformers.trainer_utils import set_seed

import accelerate
from accelerate.accelerator import Accelerator
from accelerate.state import AcceleratorState
from accelerate.test_utils.testing import (
    AccelerateTestCase,
    TempDirTestCase,
    execute_subprocess_async,
    require_cuda,
    require_fsdp,
    require_multi_gpu,
    slow,
)
from accelerate.utils.constants import (
    FSDP_AUTO_WRAP_POLICY,
    FSDP_BACKWARD_PREFETCH,
    FSDP_SHARDING_STRATEGY,
    FSDP_STATE_DICT_TYPE,
)
from accelerate.utils.dataclasses import FullyShardedDataParallelPlugin
from accelerate.utils.other import patch_environment


set_seed(4_2)

lowerCamelCase			:				Dict 			=					"bert-base-cased"
lowerCamelCase			:				Optional[Any] 			=					"fp16"
lowerCamelCase			:				Optional[int] 			=					"bf16"
lowerCamelCase			:				List[Any] 			=					[FPaa, BFaa]







@require_fsdp
@require_cuda
class 							A__   (	__snake_case  ):





		def 						A  (		self				:     List[Any]			)     ->   Optional[int]:





							'''simple docstring'''






							super().setUp()

							_SCREAMING_SNAKE_CASE							   =dict(
							    ACCELERATE_USE_FSDP='true'							, MASTER_ADDR='localhost'							, MASTER_PORT='10999'							, RANK='0'							, LOCAL_RANK='0'							, WORLD_SIZE='1'							, )





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





							'''simple docstring'''






							from torch.distributed.fsdp.fully_sharded_data_parallel import ShardingStrategy

							for i, strategy in enumerate(lowerCamelCase_			):
												_SCREAMING_SNAKE_CASE							   =self.dist_env.copy()
												_SCREAMING_SNAKE_CASE							   =f"{i + 1}"
												_SCREAMING_SNAKE_CASE							   =strategy
												with mockenv_context(**lowerCamelCase_			):
																	_SCREAMING_SNAKE_CASE							   =FullyShardedDataParallelPlugin()
																	self.assertEqual(fsdp_plugin.sharding_strategy							, ShardingStrategy(i + 1			)			)





		def 						A  (		self				:     List[Any]			)     ->   Dict:





							'''simple docstring'''






							from torch.distributed.fsdp.fully_sharded_data_parallel import BackwardPrefetch

							for i, prefetch_policy in enumerate(lowerCamelCase_			):
												_SCREAMING_SNAKE_CASE							   =self.dist_env.copy()
												_SCREAMING_SNAKE_CASE							   =prefetch_policy
												with mockenv_context(**lowerCamelCase_			):
																	_SCREAMING_SNAKE_CASE							   =FullyShardedDataParallelPlugin()
																	if prefetch_policy == "NO_PREFETCH":
																						self.assertIsNone(fsdp_plugin.backward_prefetch			)
																	else:
																						self.assertEqual(fsdp_plugin.backward_prefetch							, BackwardPrefetch(i + 1			)			)





		def 						A  (		self				:     List[str]			)     ->   Any:





							'''simple docstring'''






							from torch.distributed.fsdp.fully_sharded_data_parallel import StateDictType

							for i, state_dict_type in enumerate(lowerCamelCase_			):
												_SCREAMING_SNAKE_CASE							   =self.dist_env.copy()
												_SCREAMING_SNAKE_CASE							   =state_dict_type
												with mockenv_context(**lowerCamelCase_			):
																	_SCREAMING_SNAKE_CASE							   =FullyShardedDataParallelPlugin()
																	self.assertEqual(fsdp_plugin.state_dict_type							, StateDictType(i + 1			)			)
																	if state_dict_type == "FULL_STATE_DICT":
																						self.assertTrue(fsdp_plugin.state_dict_config.offload_to_cpu			)
																						self.assertTrue(fsdp_plugin.state_dict_config.ranka_only			)





		def 						A  (		self				:     Optional[Any]			)     ->   str:





							'''simple docstring'''






							_SCREAMING_SNAKE_CASE							   =AutoModel.from_pretrained(lowerCamelCase_			)
							for policy in FSDP_AUTO_WRAP_POLICY:
												_SCREAMING_SNAKE_CASE							   =self.dist_env.copy()
												_SCREAMING_SNAKE_CASE							   =policy
												if policy == "TRANSFORMER_BASED_WRAP":
																	_SCREAMING_SNAKE_CASE							   ="""BertLayer"""
												elif policy == "SIZE_BASED_WRAP":
																	_SCREAMING_SNAKE_CASE							   ="""2000"""
												with mockenv_context(**lowerCamelCase_			):
																	_SCREAMING_SNAKE_CASE							   =FullyShardedDataParallelPlugin()
																	fsdp_plugin.set_auto_wrap_policy(lowerCamelCase_			)
																	if policy == "NO_WRAP":
																						self.assertIsNone(fsdp_plugin.auto_wrap_policy			)
																	else:
																						self.assertIsNotNone(fsdp_plugin.auto_wrap_policy			)

							_SCREAMING_SNAKE_CASE							   =self.dist_env.copy()
							_SCREAMING_SNAKE_CASE							   ="""TRANSFORMER_BASED_WRAP"""
							_SCREAMING_SNAKE_CASE							   ="""T5Layer"""
							with mockenv_context(**lowerCamelCase_			):
												_SCREAMING_SNAKE_CASE							   =FullyShardedDataParallelPlugin()
												with self.assertRaises(lowerCamelCase_			) as cm:
																	fsdp_plugin.set_auto_wrap_policy(lowerCamelCase_			)
												self.assertTrue('Could not find the transformer layer class to wrap in the model.' in str(cm.exception			)			)

							_SCREAMING_SNAKE_CASE							   =self.dist_env.copy()
							_SCREAMING_SNAKE_CASE							   ="""SIZE_BASED_WRAP"""
							_SCREAMING_SNAKE_CASE							   ="""0"""
							with mockenv_context(**lowerCamelCase_			):
												_SCREAMING_SNAKE_CASE							   =FullyShardedDataParallelPlugin()
												fsdp_plugin.set_auto_wrap_policy(lowerCamelCase_			)
												self.assertIsNone(fsdp_plugin.auto_wrap_policy			)





		def 						A  (		self				:     Dict			)     ->   str:





							'''simple docstring'''






							from torch.distributed.fsdp.fully_sharded_data_parallel import MixedPrecision
							from torch.distributed.fsdp.sharded_grad_scaler import ShardedGradScaler

							for mp_dtype in dtypes:
												_SCREAMING_SNAKE_CASE							   =self.dist_env.copy()
												_SCREAMING_SNAKE_CASE							   =mp_dtype
												with mockenv_context(**lowerCamelCase_			):
																	_SCREAMING_SNAKE_CASE							   =Accelerator()
																	if mp_dtype == "fp16":
																						_SCREAMING_SNAKE_CASE							   =torch.floataa
																	elif mp_dtype == "bf16":
																						_SCREAMING_SNAKE_CASE							   =torch.bfloataa
																	_SCREAMING_SNAKE_CASE							   =MixedPrecision(param_dtype=lowerCamelCase_							, reduce_dtype=lowerCamelCase_							, buffer_dtype=lowerCamelCase_			)
																	self.assertEqual(accelerator.state.fsdp_plugin.mixed_precision_policy							, lowerCamelCase_			)
																	if mp_dtype == FPaa:
																						self.assertTrue(isinstance(accelerator.scaler							, lowerCamelCase_			)			)
																	elif mp_dtype == BFaa:
																						self.assertIsNone(accelerator.scaler			)
																	AcceleratorState._reset_state(lowerCamelCase_			)





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





							'''simple docstring'''






							from torch.distributed.fsdp.fully_sharded_data_parallel import CPUOffload

							for flag in [True, False]:
												_SCREAMING_SNAKE_CASE							   =self.dist_env.copy()
												_SCREAMING_SNAKE_CASE							   =str(lowerCamelCase_			).lower()
												with mockenv_context(**lowerCamelCase_			):
																	_SCREAMING_SNAKE_CASE							   =FullyShardedDataParallelPlugin()
																	self.assertEqual(fsdp_plugin.cpu_offload							, CPUOffload(offload_params=lowerCamelCase_			)			)







@require_fsdp
@require_multi_gpu
@slow
class 							A__   (	__snake_case  ):





		def 						A  (		self				:     Union[str, Any]			)     ->   Optional[int]:





							'''simple docstring'''






							super().setUp()
							_SCREAMING_SNAKE_CASE							   =0.82
							_SCREAMING_SNAKE_CASE							   =[
							    """fsdp_shard_grad_op_transformer_based_wrap""",
							    """fsdp_full_shard_transformer_based_wrap""",
							]
							_SCREAMING_SNAKE_CASE							   ={
							    """multi_gpu_fp16""": 3200,
							    """fsdp_shard_grad_op_transformer_based_wrap_fp16""": 2000,
							    """fsdp_full_shard_transformer_based_wrap_fp16""": 1900,
							    # Disabling below test as it overwhelms the RAM memory usage
							    # on CI self-hosted runner leading to tests getting killed.
							    # "fsdp_full_shard_cpu_offload_transformer_based_wrap_fp32": 1500,  # fp16 was leading to indefinite hang
							}
							_SCREAMING_SNAKE_CASE							   =160
							_SCREAMING_SNAKE_CASE							   =160

							_SCREAMING_SNAKE_CASE							   =inspect.getfile(accelerate.test_utils			)
							_SCREAMING_SNAKE_CASE							   =os.path.sep.join(mod_file.split(os.path.sep			)[:-1] + ['scripts', 'external_deps']			)





		def 						A  (		self				:     Dict			)     ->   Dict:





							'''simple docstring'''






							_SCREAMING_SNAKE_CASE							   =os.path.join(self.test_scripts_folder							, 'test_performance.py'			)
							_SCREAMING_SNAKE_CASE							   =["""accelerate""", """launch""", """--num_processes=2""", """--num_machines=1""", """--machine_rank=0""", """--use_fsdp"""]
							for config in self.performance_configs:
												_SCREAMING_SNAKE_CASE							   =cmd.copy()
												for i, strategy in enumerate(lowerCamelCase_			):
																	if strategy.lower() in config:
																						cmd_config.append(f"--fsdp_sharding_strategy={i+1}"			)
																						break

												if "fp32" in config:
																	cmd_config.append('--mixed_precision=no'			)
												else:
																	cmd_config.append('--mixed_precision=fp16'			)

												if "cpu_offload" in config:
																	cmd_config.append('--fsdp_offload_params=True'			)

												for policy in FSDP_AUTO_WRAP_POLICY:
																	if policy.lower() in config:
																						cmd_config.append(f"--fsdp_auto_wrap_policy={policy}"			)
																						break

												if policy == "TRANSFORMER_BASED_WRAP":
																	cmd_config.append('--fsdp_transformer_layer_cls_to_wrap=BertLayer'			)
												elif policy == "SIZE_BASED_WRAP":
																	cmd_config.append('--fsdp_min_num_params=2000'			)

												cmd_config.extend(
												    [
												        self.test_file_path,
												        f"--output_dir={self.tmpdir}",
												        f"--performance_lower_bound={self.performance_lower_bound}",
												    ]			)
												with patch_environment(omp_num_threads=1			):
																	execute_subprocess_async(lowerCamelCase_							, env=os.environ.copy()			)





		def 						A  (		self				:     List[Any]			)     ->   Dict:





							'''simple docstring'''






							_SCREAMING_SNAKE_CASE							   =os.path.join(self.test_scripts_folder							, 'test_checkpointing.py'			)
							_SCREAMING_SNAKE_CASE							   =[
							    """accelerate""",
							    """launch""",
							    """--num_processes=2""",
							    """--num_machines=1""",
							    """--machine_rank=0""",
							    """--use_fsdp""",
							    """--mixed_precision=fp16""",
							    """--fsdp_transformer_layer_cls_to_wrap=BertLayer""",
							]

							for i, strategy in enumerate(lowerCamelCase_			):
												_SCREAMING_SNAKE_CASE							   =cmd.copy()
												cmd_config.append(f"--fsdp_sharding_strategy={i+1}"			)
												if strategy != "FULL_SHARD":
																	continue
												_SCREAMING_SNAKE_CASE							   =len(lowerCamelCase_			)
												for state_dict_type in FSDP_STATE_DICT_TYPE:
																	_SCREAMING_SNAKE_CASE							   =cmd_config[:state_dict_config_index]
																	cmd_config.append(f"--fsdp_state_dict_type={state_dict_type}"			)
																	cmd_config.extend(
																	    [
																	        self.test_file_path,
																	        f"--output_dir={self.tmpdir}",
																	        '--partial_train_epoch=1',
																	    ]			)
																	with patch_environment(omp_num_threads=1			):
																						execute_subprocess_async(lowerCamelCase_							, env=os.environ.copy()			)

																	_SCREAMING_SNAKE_CASE							   =cmd_config[:-1]
																	_SCREAMING_SNAKE_CASE							   =os.path.join(self.tmpdir							, 'epoch_0'			)
																	cmd_config.extend(
																	    [
																	        f"--resume_from_checkpoint={resume_from_checkpoint}",
																	    ]			)
																	with patch_environment(omp_num_threads=1			):
																						execute_subprocess_async(lowerCamelCase_							, env=os.environ.copy()			)





		def 						A  (		self				:     Dict			)     ->   List[str]:





							'''simple docstring'''






							_SCREAMING_SNAKE_CASE							   =os.path.join(self.test_scripts_folder							, 'test_peak_memory_usage.py'			)
							_SCREAMING_SNAKE_CASE							   =[
							    """accelerate""",
							    """launch""",
							    """--num_processes=2""",
							    """--num_machines=1""",
							    """--machine_rank=0""",
							]
							for spec, peak_mem_upper_bound in self.peak_memory_usage_upper_bound.items():
												_SCREAMING_SNAKE_CASE							   =cmd.copy()
												if "fp16" in spec:
																	cmd_config.extend(['--mixed_precision=fp16']			)
												else:
																	cmd_config.extend(['--mixed_precision=no']			)

												if "multi_gpu" in spec:
																	continue
												else:
																	cmd_config.extend(['--use_fsdp']			)
																	for i, strategy in enumerate(lowerCamelCase_			):
																						if strategy.lower() in spec:
																											cmd_config.append(f"--fsdp_sharding_strategy={i+1}"			)
																											break

																	if "cpu_offload" in spec:
																						cmd_config.append('--fsdp_offload_params=True'			)

																	for policy in FSDP_AUTO_WRAP_POLICY:
																						if policy.lower() in spec:
																											cmd_config.append(f"--fsdp_auto_wrap_policy={policy}"			)
																											break

																	if policy == "TRANSFORMER_BASED_WRAP":
																						cmd_config.append('--fsdp_transformer_layer_cls_to_wrap=BertLayer'			)
																	elif policy == "SIZE_BASED_WRAP":
																						cmd_config.append('--fsdp_min_num_params=2000'			)

												cmd_config.extend(
												    [
												        self.test_file_path,
												        f"--output_dir={self.tmpdir}",
												        f"--peak_memory_upper_bound={peak_mem_upper_bound}",
												        f"--n_train={self.n_train}",
												        f"--n_val={self.n_val}",
												    ]			)
												with patch_environment(omp_num_threads=1			):
																	execute_subprocess_async(lowerCamelCase_							, env=os.environ.copy()			)



'''simple docstring'''
from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt


def 	_lowerCAmelCase (						_UpperCamelCase						:					int    )				->      bool:
     """simple docstring"""




     _SCREAMING_SNAKE_CASE							   =int(number**0.5    )
     return number == sq * sq


def 	_lowerCAmelCase (						_UpperCamelCase						:					int							,			_UpperCamelCase						:					int							,			_UpperCamelCase						:					int							,			_UpperCamelCase						:					int							,			_UpperCamelCase						:					int							,			_UpperCamelCase						:					int    )				->      tuple[int, int]:
     """simple docstring"""




     _SCREAMING_SNAKE_CASE							   =x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
     _SCREAMING_SNAKE_CASE							   =x_den * y_den * z_den
     _SCREAMING_SNAKE_CASE							   =gcd(_UpperCamelCase							,			_UpperCamelCase    )
     top //= hcf
     bottom //= hcf
     return top, bottom


def 	_lowerCAmelCase (						_UpperCamelCase						:					int = 35    )				->      int:
     """simple docstring"""




     _SCREAMING_SNAKE_CASE							   =set()
     _SCREAMING_SNAKE_CASE							   =42
     _SCREAMING_SNAKE_CASE							   =Fraction(0    )
     _SCREAMING_SNAKE_CASE							   =42

     for x_num in range(1							,			order + 1    ):
          for x_den in range(x_num + 1							,			order + 1    ):
               for y_num in range(1							,			order + 1    ):
                    for y_den in range(y_num + 1							,			order + 1    ):
                         # n=1
                         _SCREAMING_SNAKE_CASE							   =x_num * y_den + x_den * y_num
                         _SCREAMING_SNAKE_CASE							   =x_den * y_den
                         _SCREAMING_SNAKE_CASE							   =gcd(_UpperCamelCase							,			_UpperCamelCase    )
                         z_num //= hcf
                         z_den //= hcf
                         if 0 < z_num < z_den <= order:
                              _SCREAMING_SNAKE_CASE							   =add_three(
                                  _UpperCamelCase							,			_UpperCamelCase							,			_UpperCamelCase							,			_UpperCamelCase							,			_UpperCamelCase							,			_UpperCamelCase    )
                              unique_s.add(_UpperCamelCase    )

                         # n=2
                         _SCREAMING_SNAKE_CASE							   =(
                             x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
                         )
                         _SCREAMING_SNAKE_CASE							   =x_den * x_den * y_den * y_den
                         if is_sq(_UpperCamelCase    ) and is_sq(_UpperCamelCase    ):
                              _SCREAMING_SNAKE_CASE							   =int(sqrt(_UpperCamelCase    )    )
                              _SCREAMING_SNAKE_CASE							   =int(sqrt(_UpperCamelCase    )    )
                              _SCREAMING_SNAKE_CASE							   =gcd(_UpperCamelCase							,			_UpperCamelCase    )
                              z_num //= hcf
                              z_den //= hcf
                              if 0 < z_num < z_den <= order:
                                   _SCREAMING_SNAKE_CASE							   =add_three(
                                       _UpperCamelCase							,			_UpperCamelCase							,			_UpperCamelCase							,			_UpperCamelCase							,			_UpperCamelCase							,			_UpperCamelCase    )
                                   unique_s.add(_UpperCamelCase    )

                    # n=-1
                         _SCREAMING_SNAKE_CASE							   =x_num * y_num
                         _SCREAMING_SNAKE_CASE							   =x_den * y_num + x_num * y_den
                         _SCREAMING_SNAKE_CASE							   =gcd(_UpperCamelCase							,			_UpperCamelCase    )
                         z_num //= hcf
                         z_den //= hcf
                         if 0 < z_num < z_den <= order:
                              _SCREAMING_SNAKE_CASE							   =add_three(
                                  _UpperCamelCase							,			_UpperCamelCase							,			_UpperCamelCase							,			_UpperCamelCase							,			_UpperCamelCase							,			_UpperCamelCase    )
                              unique_s.add(_UpperCamelCase    )

                         # n=2
                         _SCREAMING_SNAKE_CASE							   =x_num * x_num * y_num * y_num
                         _SCREAMING_SNAKE_CASE							   =(
                             x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
                         )
                         if is_sq(_UpperCamelCase    ) and is_sq(_UpperCamelCase    ):
                              _SCREAMING_SNAKE_CASE							   =int(sqrt(_UpperCamelCase    )    )
                              _SCREAMING_SNAKE_CASE							   =int(sqrt(_UpperCamelCase    )    )
                              _SCREAMING_SNAKE_CASE							   =gcd(_UpperCamelCase							,			_UpperCamelCase    )
                              z_num //= hcf
                              z_den //= hcf
                              if 0 < z_num < z_den <= order:
                                   _SCREAMING_SNAKE_CASE							   =add_three(
                                       _UpperCamelCase							,			_UpperCamelCase							,			_UpperCamelCase							,			_UpperCamelCase							,			_UpperCamelCase							,			_UpperCamelCase    )
                                   unique_s.add(_UpperCamelCase    )

     for num, den in unique_s:
          total += Fraction(_UpperCamelCase							,			_UpperCamelCase    )

     return total.denominator + total.numerator


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