





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			:	Optional[int]					    =	logging.get_logger(__name__)



class    A__  (			__snake_case     ):
      _UpperCAmelCase      :List[Any]		       =  'linear'
      _UpperCAmelCase      :Optional[Any]		       =  'cosine'
      _UpperCAmelCase      :List[str]		       =  'cosine_with_restarts'
      _UpperCAmelCase      :Dict		       =  'polynomial'
      _UpperCAmelCase      :Union[str, Any]		       =  'constant'
      _UpperCAmelCase      :Any		       =  'constant_with_warmup'
      _UpperCAmelCase      :Optional[int]		       =  'piecewise_constant'



def 						A_							(	_lowerCAmelCase				,  _lowerCAmelCase = -1	)		->					Dict:
 return LambdaLR(_lowerCAmelCase				,  lambda _lowerCAmelCase	: 1				,  last_epoch=_lowerCAmelCase	)



def 						A_							(	_lowerCAmelCase				,  _lowerCAmelCase				,  _lowerCAmelCase = -1	)		->					Any:

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

 return LambdaLR(_lowerCAmelCase				,  _lowerCAmelCase				,  last_epoch=_lowerCAmelCase	)



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

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

  return rule_func

 UpperCamelCase      :   Optional[int]			      =  create_rules_function(_lowerCAmelCase				,  _lowerCAmelCase	)

 return LambdaLR(_lowerCAmelCase				,  _lowerCAmelCase				,  last_epoch=_lowerCAmelCase	)



def 						A_							(	_lowerCAmelCase				,  _lowerCAmelCase				,  _lowerCAmelCase				,  _lowerCAmelCase=-1	)		->					Any:

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

 return LambdaLR(_lowerCAmelCase				,  _lowerCAmelCase				,  _lowerCAmelCase	)



def 						A_							(	_lowerCAmelCase				,  _lowerCAmelCase				,  _lowerCAmelCase				,  _lowerCAmelCase = 0.5				,  _lowerCAmelCase = -1	)		->					Any:

 def lr_lambda(_lowerCAmelCase	):
  if current_step < num_warmup_steps:
   return float(_lowerCAmelCase	) / float(max(1				,  _lowerCAmelCase	)	)
  UpperCamelCase      :   str			      =  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(_lowerCAmelCase	) * 2.0 * progress	))	)

 return LambdaLR(_lowerCAmelCase				,  _lowerCAmelCase				,  _lowerCAmelCase	)



def 						A_							(	_lowerCAmelCase				,  _lowerCAmelCase				,  _lowerCAmelCase				,  _lowerCAmelCase = 1				,  _lowerCAmelCase = -1	)		->					int:

 def lr_lambda(_lowerCAmelCase	):
  if current_step < num_warmup_steps:
   return float(_lowerCAmelCase	) / float(max(1				,  _lowerCAmelCase	)	)
  UpperCamelCase      :   Tuple			      =  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(_lowerCAmelCase	) * progress) % 1.0)	))	)

 return LambdaLR(_lowerCAmelCase				,  _lowerCAmelCase				,  _lowerCAmelCase	)



def 						A_							(	_lowerCAmelCase				,  _lowerCAmelCase				,  _lowerCAmelCase				,  _lowerCAmelCase=1e-7				,  _lowerCAmelCase=1.0				,  _lowerCAmelCase=-1	)		->					str:
 UpperCamelCase      :   List[str]			      =  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(_lowerCAmelCase	):
  if current_step < num_warmup_steps:
   return float(_lowerCAmelCase	) / float(max(1				,  _lowerCAmelCase	)	)
  elif current_step > num_training_steps:
   return lr_end / lr_init  # as LambdaLR multiplies by lr_init
  else:
   UpperCamelCase      :   Tuple			      =  lr_init - lr_end
   UpperCamelCase      :   Optional[int]			      =  num_training_steps - num_warmup_steps
   UpperCamelCase      :   int			      =  1 - (current_step - num_warmup_steps) / decay_steps
   UpperCamelCase      :   Tuple			      =  lr_range * pct_remaining**power + lr_end
   return decay / lr_init  # as LambdaLR multiplies by lr_init

 return LambdaLR(_lowerCAmelCase				,  _lowerCAmelCase				,  _lowerCAmelCase	)


__lowerCamelCase			:	List[str]					    =	{
    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_							(	_lowerCAmelCase				,  _lowerCAmelCase				,  _lowerCAmelCase = None				,  _lowerCAmelCase = None				,  _lowerCAmelCase = None				,  _lowerCAmelCase = 1				,  _lowerCAmelCase = 1.0				,  _lowerCAmelCase = -1				,  )		->					Dict:
 UpperCamelCase      :   List[str]			      =  SchedulerType(_lowerCAmelCase	)
 UpperCamelCase      :   Optional[Any]			      =  TYPE_TO_SCHEDULER_FUNCTION[name]
 if name == SchedulerType.CONSTANT:
  return schedule_func(_lowerCAmelCase				,  last_epoch=_lowerCAmelCase	)

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

 # 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(_lowerCAmelCase				,  num_warmup_steps=_lowerCAmelCase				,  last_epoch=_lowerCAmelCase	)

 # 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(
      _lowerCAmelCase				,  num_warmup_steps=_lowerCAmelCase				,  num_training_steps=_lowerCAmelCase				,  num_cycles=_lowerCAmelCase				,  last_epoch=_lowerCAmelCase				,  )

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

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







def 						A_							(	_lowerCAmelCase	)		->					bool:
 return str(_lowerCAmelCase	) == str(_lowerCAmelCase	)[::-1]



def 						A_							(	_lowerCAmelCase	)		->					int:
 return int(_lowerCAmelCase	) + int(str(_lowerCAmelCase	)[::-1]	)



def 						A_							(	_lowerCAmelCase = 1_0000	)		->					int:
 UpperCamelCase      :   List[Any]			      =  []
 for num in range(1				,  _lowerCAmelCase	):
  UpperCamelCase      :   Union[str, Any]			      =  0
  UpperCamelCase      :   List[str]			      =  num
  while iterations < 50:
   UpperCamelCase      :   int			      =  sum_reverse(_lowerCAmelCase	)
   iterations += 1
   if is_palindrome(_lowerCAmelCase	):
    break
  else:
   lychrel_nums.append(_lowerCAmelCase	)
 return len(_lowerCAmelCase	)


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