
'''simple docstring'''
import math
from enum import Enum
from typing import Optional, Union

from torch.optim import Optimizer
from torch.optim.lr_scheduler import LambdaLR

from .utils import logging


__lowerCAmelCase												=	logging.get_logger(__name__)


class       _lowerCAmelCase   (   __snake_case				):







							'''simple docstring'''

							lowerCAmelCase_ 						=						"linear"
							lowerCAmelCase_ 						=						"cosine"
							lowerCAmelCase_ 						=						"cosine_with_restarts"
							lowerCAmelCase_ 						=						"polynomial"
							lowerCAmelCase_ 						=						"constant"
							lowerCAmelCase_ 						=						"constant_with_warmup"
							lowerCAmelCase_ 						=						"piecewise_constant"






def  __SCREAMING_SNAKE_CASE				(  _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE = -1				):
							return LambdaLR(_SCREAMING_SNAKE_CASE							, lambda _SCREAMING_SNAKE_CASE				: 1							, last_epoch=_SCREAMING_SNAKE_CASE				)






def  __SCREAMING_SNAKE_CASE				(  _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE = -1				):

							def lr_lambda(_SCREAMING_SNAKE_CASE				):
														if current_step < num_warmup_steps:
																					return float(_SCREAMING_SNAKE_CASE				) / float(max(1.0							, _SCREAMING_SNAKE_CASE				)				)
														return 1.0

							return LambdaLR(_SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE							, last_epoch=_SCREAMING_SNAKE_CASE				)






def  __SCREAMING_SNAKE_CASE				(  _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE = -1				):
							_snake_case       =  {}
							_snake_case       =  step_rules.split(""","""				)
							for rule_str in rule_list[:-1]:
														_snake_case,							_snake_case       =  rule_str.split(""":"""				)
														_snake_case       =  int(_SCREAMING_SNAKE_CASE				)
														_snake_case       =  float(_SCREAMING_SNAKE_CASE				)
														_snake_case       =  value
							_snake_case       =  float(rule_list[-1]				)

							def create_rules_function(_SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE				):
														def rule_func(_SCREAMING_SNAKE_CASE				) -> float:
																					_snake_case       =  sorted(rules_dict.keys()				)
																					for i, sorted_step in enumerate(_SCREAMING_SNAKE_CASE				):
																												if steps < sorted_step:
																																			return rules_dict[sorted_steps[i]]
																					return last_lr_multiple

														return rule_func

							_snake_case       =  create_rules_function(_SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE				)

							return LambdaLR(_SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE							, last_epoch=_SCREAMING_SNAKE_CASE				)






def  __SCREAMING_SNAKE_CASE				(  _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE=-1				):

							def lr_lambda(_SCREAMING_SNAKE_CASE				):
														if current_step < num_warmup_steps:
																					return float(_SCREAMING_SNAKE_CASE				) / float(max(1							, _SCREAMING_SNAKE_CASE				)				)
														return max(
														    0.0							, float(num_training_steps - current_step				) / float(max(1							, num_training_steps - num_warmup_steps				)				)				)

							return LambdaLR(_SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE				)






def  __SCREAMING_SNAKE_CASE				(  _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE = 0.5							, _SCREAMING_SNAKE_CASE = -1				):

							def lr_lambda(_SCREAMING_SNAKE_CASE				):
														if current_step < num_warmup_steps:
																					return float(_SCREAMING_SNAKE_CASE				) / float(max(1							, _SCREAMING_SNAKE_CASE				)				)
														_snake_case       =  float(current_step - num_warmup_steps				) / float(max(1							, num_training_steps - num_warmup_steps				)				)
														return max(0.0							, 0.5 * (1.0 + math.cos(math.pi * float(_SCREAMING_SNAKE_CASE				) * 2.0 * progress				))				)

							return LambdaLR(_SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE				)






def  __SCREAMING_SNAKE_CASE				(  _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE = 1							, _SCREAMING_SNAKE_CASE = -1				):

							def lr_lambda(_SCREAMING_SNAKE_CASE				):
														if current_step < num_warmup_steps:
																					return float(_SCREAMING_SNAKE_CASE				) / float(max(1							, _SCREAMING_SNAKE_CASE				)				)
														_snake_case       =  float(current_step - num_warmup_steps				) / float(max(1							, num_training_steps - num_warmup_steps				)				)
														if progress >= 1.0:
																					return 0.0
														return max(0.0							, 0.5 * (1.0 + math.cos(math.pi * ((float(_SCREAMING_SNAKE_CASE				) * progress) % 1.0)				))				)

							return LambdaLR(_SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE				)






def  __SCREAMING_SNAKE_CASE				(  _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE=1E-7							, _SCREAMING_SNAKE_CASE=1.0							, _SCREAMING_SNAKE_CASE=-1				):
							_snake_case       =  optimizer.defaults["""lr"""]
							if not (lr_init > lr_end):
														raise ValueError(f"""lr_end ({lr_end}) must be be smaller than initial lr ({lr_init})"""				)

							def lr_lambda(_SCREAMING_SNAKE_CASE				):
														if current_step < num_warmup_steps:
																					return float(_SCREAMING_SNAKE_CASE				) / float(max(1							, _SCREAMING_SNAKE_CASE				)				)
														elif current_step > num_training_steps:
																					return lr_end / lr_init  # as LambdaLR multiplies by lr_init
														else:
																					_snake_case       =  lr_init - lr_end
																					_snake_case       =  num_training_steps - num_warmup_steps
																					_snake_case       =  1 - (current_step - num_warmup_steps) / decay_steps
																					_snake_case       =  lr_range * pct_remaining**power + lr_end
																					return decay / lr_init  # as LambdaLR multiplies by lr_init

							return LambdaLR(_SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE				)


__lowerCAmelCase												=	{
    SchedulerType.LINEAR: get_linear_schedule_with_warmup,
    SchedulerType.COSINE: get_cosine_schedule_with_warmup,
    SchedulerType.COSINE_WITH_RESTARTS: get_cosine_with_hard_restarts_schedule_with_warmup,
    SchedulerType.POLYNOMIAL: get_polynomial_decay_schedule_with_warmup,
    SchedulerType.CONSTANT: get_constant_schedule,
    SchedulerType.CONSTANT_WITH_WARMUP: get_constant_schedule_with_warmup,
    SchedulerType.PIECEWISE_CONSTANT: get_piecewise_constant_schedule,
}






def  __SCREAMING_SNAKE_CASE				(  _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE = None							, _SCREAMING_SNAKE_CASE = None							, _SCREAMING_SNAKE_CASE = None							, _SCREAMING_SNAKE_CASE = 1							, _SCREAMING_SNAKE_CASE = 1.0							, _SCREAMING_SNAKE_CASE = -1							, ):
							_snake_case       =  SchedulerType(_SCREAMING_SNAKE_CASE				)
							_snake_case       =  TYPE_TO_SCHEDULER_FUNCTION[name]
							if name == SchedulerType.CONSTANT:
														return schedule_func(_SCREAMING_SNAKE_CASE							, last_epoch=_SCREAMING_SNAKE_CASE				)

							if name == SchedulerType.PIECEWISE_CONSTANT:
														return schedule_func(_SCREAMING_SNAKE_CASE							, step_rules=_SCREAMING_SNAKE_CASE							, last_epoch=_SCREAMING_SNAKE_CASE				)

							# All other schedulers require `num_warmup_steps`
							if num_warmup_steps is None:
														raise ValueError(f"""{name} requires `num_warmup_steps`, please provide that argument."""				)

							if name == SchedulerType.CONSTANT_WITH_WARMUP:
														return schedule_func(_SCREAMING_SNAKE_CASE							, num_warmup_steps=_SCREAMING_SNAKE_CASE							, last_epoch=_SCREAMING_SNAKE_CASE				)

							# All other schedulers require `num_training_steps`
							if num_training_steps is None:
														raise ValueError(f"""{name} requires `num_training_steps`, please provide that argument."""				)

							if name == SchedulerType.COSINE_WITH_RESTARTS:
														return schedule_func(
														    _SCREAMING_SNAKE_CASE							, num_warmup_steps=_SCREAMING_SNAKE_CASE							, num_training_steps=_SCREAMING_SNAKE_CASE							, num_cycles=_SCREAMING_SNAKE_CASE							, last_epoch=_SCREAMING_SNAKE_CASE							, )

							if name == SchedulerType.POLYNOMIAL:
														return schedule_func(
														    _SCREAMING_SNAKE_CASE							, num_warmup_steps=_SCREAMING_SNAKE_CASE							, num_training_steps=_SCREAMING_SNAKE_CASE							, power=_SCREAMING_SNAKE_CASE							, last_epoch=_SCREAMING_SNAKE_CASE							, )

							return schedule_func(
							    _SCREAMING_SNAKE_CASE							, num_warmup_steps=_SCREAMING_SNAKE_CASE							, num_training_steps=_SCREAMING_SNAKE_CASE							, last_epoch=_SCREAMING_SNAKE_CASE				)

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

import typing
from collections import Counter






def  __SCREAMING_SNAKE_CASE				(  _SCREAMING_SNAKE_CASE				):
							_snake_case       =  Counter()
							for base in range(1							, max_perimeter + 1				):
														for perpendicular in range(_SCREAMING_SNAKE_CASE							, max_perimeter + 1				):
																					_snake_case       =  (base * base + perpendicular * perpendicular) ** 0.5
																					if hypotenuse == int(_SCREAMING_SNAKE_CASE				):
																												_snake_case       =  int(base + perpendicular + hypotenuse				)
																												if perimeter > max_perimeter:
																																			continue
																												triplets[perimeter] += 1
							return triplets






def  __SCREAMING_SNAKE_CASE				(  _SCREAMING_SNAKE_CASE = 1000				):
							_snake_case       =  pythagorean_triple(_SCREAMING_SNAKE_CASE				)
							return triplets.most_common(1				)[0][0]


if __name__ == "__main__":
				print(f'''Perimeter {solution()} has maximum solutions''')