





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


__UpperCAmelCase       :   str				       =							logging.get_logger(__name__)







class     __snake_case       (							__lowerCamelCase			):





       '''simple docstring'''







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







def 			A__							(    SCREAMING_SNAKE_CASE__					,					SCREAMING_SNAKE_CASE__ = -1)   ->    Any:
  return LambdaLR(SCREAMING_SNAKE_CASE__					,					lambda SCREAMING_SNAKE_CASE__: 1					,					last_epoch=SCREAMING_SNAKE_CASE__)







def 			A__							(    SCREAMING_SNAKE_CASE__					,					SCREAMING_SNAKE_CASE__					,					SCREAMING_SNAKE_CASE__ = -1)   ->    Optional[int]:

  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 			A__							(    SCREAMING_SNAKE_CASE__					,					SCREAMING_SNAKE_CASE__					,					SCREAMING_SNAKE_CASE__ = -1)   ->    Tuple:
  __snake_case:						str   =						{}
  __snake_case:						Union[str, Any]   =						step_rules.split(""",""")
  for rule_str in rule_list[:-1]:
    __snake_case  ,   __snake_case:						Optional[int]   =						rule_str.split(""":""")
    __snake_case:						Dict   =						int(SCREAMING_SNAKE_CASE__)
    __snake_case:						int   =						float(SCREAMING_SNAKE_CASE__)
    __snake_case:						Optional[Any]   =						value
  __snake_case:						List[str]   =						float(rule_list[-1])

  def create_rules_function(SCREAMING_SNAKE_CASE__					,					SCREAMING_SNAKE_CASE__):
    def rule_func(SCREAMING_SNAKE_CASE__) -> float:
      __snake_case:						Union[str, Any]   =						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:						List[Any]   =						create_rules_function(SCREAMING_SNAKE_CASE__					,					SCREAMING_SNAKE_CASE__)

  return LambdaLR(SCREAMING_SNAKE_CASE__					,					SCREAMING_SNAKE_CASE__					,					last_epoch=SCREAMING_SNAKE_CASE__)







def 			A__							(    SCREAMING_SNAKE_CASE__					,					SCREAMING_SNAKE_CASE__					,					SCREAMING_SNAKE_CASE__					,					SCREAMING_SNAKE_CASE__=-1)   ->    Dict:

  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 			A__							(    SCREAMING_SNAKE_CASE__					,					SCREAMING_SNAKE_CASE__					,					SCREAMING_SNAKE_CASE__					,					SCREAMING_SNAKE_CASE__ = 0.5					,					SCREAMING_SNAKE_CASE__ = -1)   ->    Tuple:

  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:						Any   =						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 			A__							(    SCREAMING_SNAKE_CASE__					,					SCREAMING_SNAKE_CASE__					,					SCREAMING_SNAKE_CASE__					,					SCREAMING_SNAKE_CASE__ = 1					,					SCREAMING_SNAKE_CASE__ = -1)   ->    List[Any]:

  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:						Any   =						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 			A__							(    SCREAMING_SNAKE_CASE__					,					SCREAMING_SNAKE_CASE__					,					SCREAMING_SNAKE_CASE__					,					SCREAMING_SNAKE_CASE__=1e-7					,					SCREAMING_SNAKE_CASE__=1.0					,					SCREAMING_SNAKE_CASE__=-1)   ->    Dict:
  __snake_case:						Any   =						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:						List[str]   =						lr_init - lr_end
      __snake_case:						Any   =						num_training_steps - num_warmup_steps
      __snake_case:						Any   =						1 - (current_step - num_warmup_steps) / decay_steps
      __snake_case:						Any   =						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__)


__UpperCAmelCase       :   Optional[int]				       =							{
    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 			A__							(    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					,					)   ->    Any:
  __snake_case:						List[str]   =						SchedulerType(SCREAMING_SNAKE_CASE__)
  __snake_case:						Any   =						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__)













from __future__ import annotations

import typing
from collections import Counter







def 			A__							(    SCREAMING_SNAKE_CASE__)   ->    typing.Counter[int]:
  __snake_case:						typing.Counter[int]   =						Counter()
  for base in range(1					,					max_perimeter + 1):
    for perpendicular in range(SCREAMING_SNAKE_CASE__					,					max_perimeter + 1):
      __snake_case:						Dict   =						(base * base + perpendicular * perpendicular) ** 0.5
      if hypotenuse == int(SCREAMING_SNAKE_CASE__):
        __snake_case:						Any   =						int(base + perpendicular + hypotenuse)
        if perimeter > max_perimeter:
          continue
        triplets[perimeter] += 1
  return triplets







def 			A__							(    SCREAMING_SNAKE_CASE__ = 1000)   ->    int:
  __snake_case:						List[str]   =						pythagorean_triple(SCREAMING_SNAKE_CASE__)
  return triplets.most_common(1)[0][0]


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






