


def 			lowerCAmelCase (		lowerCAmelCase_ = 50 )-> int:
				lowerCAmelCase_ :      List[str]    				=				[1] * (length + 1)

				for row_length in range(length + 1 ):
								for tile_length in range(2 ,   5 ):
												for tile_start in range(row_length - tile_length + 1 ):
																ways_number[row_length] += ways_number[
																    row_length - tile_start - tile_length
																]

				return ways_number[length]


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



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			:  Tuple     =logging.get_logger(__name__)







class 				snake_case__(							UpperCAmelCase__							):







						'''simple docstring'''




						SCREAMING_SNAKE_CASE__      :  List[str]					=							"""linear"""
						SCREAMING_SNAKE_CASE__      :  Union[str, Any]					=							"""cosine"""
						SCREAMING_SNAKE_CASE__      :  Dict					=							"""cosine_with_restarts"""
						SCREAMING_SNAKE_CASE__      :  List[str]					=							"""polynomial"""
						SCREAMING_SNAKE_CASE__      :  Dict					=							"""constant"""
						SCREAMING_SNAKE_CASE__      :  List[str]					=							"""constant_with_warmup"""
						SCREAMING_SNAKE_CASE__      :  str					=							"""piecewise_constant"""






def 			lowerCAmelCase (		lowerCAmelCase_ ,   lowerCAmelCase_ = -1 )-> Tuple:
				return LambdaLR(lowerCAmelCase_ ,   lambda lowerCAmelCase_ : 1 ,   last_epoch=lowerCAmelCase_ )



def 			lowerCAmelCase (		lowerCAmelCase_ ,   lowerCAmelCase_ ,   lowerCAmelCase_ = -1 )-> List[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 			lowerCAmelCase (		lowerCAmelCase_ ,   lowerCAmelCase_ ,   lowerCAmelCase_ = -1 )-> int:
				lowerCAmelCase_ :      Optional[int]    				=				{}
				lowerCAmelCase_ :      Union[str, Any]    				=				step_rules.split(''',''' )
				for rule_str in rule_list[:-1]:
								lowerCAmelCase_				,  lowerCAmelCase_ :      str    				=				rule_str.split(''':''' )
								lowerCAmelCase_ :      int    				=				int(lowerCAmelCase_ )
								lowerCAmelCase_ :      str    				=				float(lowerCAmelCase_ )
								lowerCAmelCase_ :      List[Any]    				=				value
				lowerCAmelCase_ :      int    				=				float(rule_list[-1] )

				def create_rules_function(lowerCAmelCase_ ,   lowerCAmelCase_ ):
								def rule_func(lowerCAmelCase_ ) -> float:
												lowerCAmelCase_ :      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

				lowerCAmelCase_ :      Tuple    				=				create_rules_function(lowerCAmelCase_ ,   lowerCAmelCase_ )

				return LambdaLR(lowerCAmelCase_ ,   lowerCAmelCase_ ,   last_epoch=lowerCAmelCase_ )



def 			lowerCAmelCase (		lowerCAmelCase_ ,   lowerCAmelCase_ ,   lowerCAmelCase_ ,   lowerCAmelCase_=-1 )-> Optional[int]:

				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 			lowerCAmelCase (		lowerCAmelCase_ ,   lowerCAmelCase_ ,   lowerCAmelCase_ ,   lowerCAmelCase_ = 0.5 ,   lowerCAmelCase_ = -1 )-> List[Any]:

				def lr_lambda(lowerCAmelCase_ ):
								if current_step < num_warmup_steps:
												return float(lowerCAmelCase_ ) / float(max(1 ,   lowerCAmelCase_ ) )
								lowerCAmelCase_ :      Tuple    				=				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 			lowerCAmelCase (		lowerCAmelCase_ ,   lowerCAmelCase_ ,   lowerCAmelCase_ ,   lowerCAmelCase_ = 1 ,   lowerCAmelCase_ = -1 )-> Dict:

				def lr_lambda(lowerCAmelCase_ ):
								if current_step < num_warmup_steps:
												return float(lowerCAmelCase_ ) / float(max(1 ,   lowerCAmelCase_ ) )
								lowerCAmelCase_ :      List[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(lowerCAmelCase_ ) * progress) % 1.0) )) )

				return LambdaLR(lowerCAmelCase_ ,   lowerCAmelCase_ ,   lowerCAmelCase_ )



def 			lowerCAmelCase (		lowerCAmelCase_ ,   lowerCAmelCase_ ,   lowerCAmelCase_ ,   lowerCAmelCase_=1e-7 ,   lowerCAmelCase_=1.0 ,   lowerCAmelCase_=-1 )-> Any:
				lowerCAmelCase_ :      Dict    				=				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:
												lowerCAmelCase_ :      List[Any]    				=				lr_init - lr_end
												lowerCAmelCase_ :      Optional[Any]    				=				num_training_steps - num_warmup_steps
												lowerCAmelCase_ :      Any    				=				1 - (current_step - num_warmup_steps) / decay_steps
												lowerCAmelCase_ :      List[Any]    				=				lr_range * pct_remaining**power + lr_end
												return decay / lr_init  # as LambdaLR multiplies by lr_init

				return LambdaLR(lowerCAmelCase_ ,   lowerCAmelCase_ ,   lowerCAmelCase_ )


_UpperCAmelCase			:  Union[str, Any]     ={
    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 			lowerCAmelCase (		lowerCAmelCase_ ,   lowerCAmelCase_ ,   lowerCAmelCase_ = None ,   lowerCAmelCase_ = None ,   lowerCAmelCase_ = None ,   lowerCAmelCase_ = 1 ,   lowerCAmelCase_ = 1.0 ,   lowerCAmelCase_ = -1 ,   )-> Optional[int]:
				lowerCAmelCase_ :      Union[str, Any]    				=				SchedulerType(lowerCAmelCase_ )
				lowerCAmelCase_ :      Optional[int]    				=				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_ )