def A__  (			lowercase:     int,		lowercase:     list					)				->		Dict:
       _enforce_args(lowercase,		lowercase					)
       if n == 0:
              return 0
       A						:     Optional[int]         =float('-inf'					)
       for i in range(1,		n + 1					):
              A						:     Union[str, Any]         =max(
                  lowercase,		prices[i - 1] + naive_cut_rod_recursive(n - i,		lowercase					)					)

       return max_revue



def A__  (			lowercase:     int,		lowercase:     list					)				->		Optional[Any]:
       _enforce_args(lowercase,		lowercase					)
       A						:     Dict         =[float('-inf'					) for _ in range(n + 1					)]
       return _top_down_cut_rod_recursive(lowercase,		lowercase,		lowercase					)



def A__  (			lowercase:     int,		lowercase:     list,		lowercase:     list					)				->		Optional[Any]:
       if max_rev[n] >= 0:
              return max_rev[n]
       elif n == 0:
              return 0
       else:
              A						:     Dict         =float('-inf'					)
              for i in range(1,		n + 1					):
                     A						:     int         =max(
                         lowercase,		prices[i - 1] + _top_down_cut_rod_recursive(n - i,		lowercase,		lowercase					),		)

              A						:     str         =max_revenue

       return max_rev[n]



def A__  (			lowercase:     int,		lowercase:     list					)				->		Optional[int]:
       _enforce_args(lowercase,		lowercase					)

       # length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
       # length 0.
       A						:     Dict         =[float('-inf'					) for _ in range(n + 1					)]
       A						:     List[Any]         =0

       for i in range(1,		n + 1					):
              A						:     Dict         =max_rev[i]
              for j in range(1,		i + 1					):
                     A						:     List[str]         =max(lowercase,		prices[j - 1] + max_rev[i - j]					)

              A						:     int         =max_revenue_i

       return max_rev[n]



def A__  (			lowercase:     int,		lowercase:     list					)				->		int:
       if n < 0:
              A						:     Tuple         =F'n must be greater than or equal to 0. Got n = {n}'
              raise ValueError(lowercase					)

       if n > len(lowercase					):
              A						:     Dict         =(
                  'Each integral piece of rod must have a corresponding price. '
                  F'Got n = {n} but length of prices = {len(lowercase					)}'
              )
              raise ValueError(lowercase					)



def A__  (			)				->		List[str]:
       A						:     Optional[Any]         =[6, 10, 12, 15, 20, 23]
       A						:     List[str]         =len(lowercase					)

       # the best revenue comes from cutting the rod into 6 pieces, each
       # of length 1 resulting in a revenue of 6 * 6 = 36.
       A						:     Union[str, Any]         =36

       A						:     Dict         =top_down_cut_rod(lowercase,		lowercase					)
       A						:     Tuple         =bottom_up_cut_rod(lowercase,		lowercase					)
       A						:     Union[str, Any]         =naive_cut_rod_recursive(lowercase,		lowercase					)

       assert expected_max_revenue == max_rev_top_down
       assert max_rev_top_down == max_rev_bottom_up
       assert max_rev_bottom_up == max_rev_naive


if __name__ == "__main__":
    main()







import logging
from dataclasses import dataclass, field
from typing import Optional

from seqaseq_trainer import arg_to_scheduler

from transformers import TrainingArguments


_lowercase							:      Any      							=logging.getLogger(__name__)



@dataclass
class  SCREAMING_SNAKE_CASE_ (					lowerCAmelCase_			):
  '''simple docstring'''


  lowercase		:     Optional[float]            =				field(
      default=0.0   ,						metadata={"help": "The label smoothing epsilon to apply (if not zero)."}			)
  lowercase		:     bool            =				field(default=lowerCAmelCase_   ,						metadata={"help": "Whether to SortishSamler or not."}			)
  lowercase		:     bool            =				field(
      default=lowerCAmelCase_   ,						metadata={"help": "Whether to use generate to calculate generative metrics (ROUGE, BLEU)."}			)
  lowercase		:     bool            =				field(default=lowerCAmelCase_   ,						metadata={"help": "whether to use adafactor"}			)
  lowercase		:     Optional[float]            =				field(
      default=lowerCAmelCase_   ,						metadata={"help": "Encoder layer dropout probability. Goes into model.config."}			)
  lowercase		:     Optional[float]            =				field(
      default=lowerCAmelCase_   ,						metadata={"help": "Decoder layer dropout probability. Goes into model.config."}			)
  lowercase		:     Optional[float]            =				field(default=lowerCAmelCase_   ,						metadata={"help": "Dropout probability. Goes into model.config."}			)
  lowercase		:     Optional[float]            =				field(
      default=lowerCAmelCase_   ,						metadata={"help": "Attention dropout probability. Goes into model.config."}			)
  lowercase		:     Optional[str]            =				field(
      default="linear"   ,						metadata={"help": f'Which lr scheduler to use. Selected in {sorted(arg_to_scheduler.keys()			)}'}   ,						)






