
lowercase__		:Tuple   =    range(2, 20 + 1)
lowercase__		:Optional[int]   =    [10**k for k in range(ks[-1] + 1)]
lowercase__		:Any   =    {}



def        UpperCamelCase    (							lowerCAmelCase__ ,			lowerCAmelCase__ ,			lowerCAmelCase__ ,			lowerCAmelCase__		):
					'''simple docstring'''
					lowercase							=						sum(a_i[j] for j in range(__UpperCamelCase ,			len(__UpperCamelCase		)		)		)
					lowercase							=						sum(a_i[j] * base[j] for j in range(min(len(__UpperCamelCase		) ,			__UpperCamelCase		)		)		)

					lowercase	,						lowercase							=						0, 0
					lowercase							=						n - i

					lowercase							=						memo.get(__UpperCamelCase		)

					if sub_memo is not None:
										lowercase							=						sub_memo.get(__UpperCamelCase		)

										if jumps is not None and len(__UpperCamelCase		) > 0:
															# find and make the largest jump without going over
															lowercase							=						-1
															for _k in range(len(__UpperCamelCase		) - 1 ,			-1 ,			-1		):
																				if jumps[_k][2] <= k and jumps[_k][1] <= max_dn:
																									lowercase							=						_k
																									break

															if max_jump >= 0:
																				lowercase	,						lowercase	,						lowercase							=						jumps[max_jump]
																				# since the difference between jumps is cached, add c
																				lowercase							=						diff + c
																				for j in range(min(__UpperCamelCase ,			len(__UpperCamelCase		)		)		):
																									lowercase	,						lowercase							=						divmod(__UpperCamelCase ,			10		)
																				if new_c > 0:
																									add(__UpperCamelCase ,			__UpperCamelCase ,			__UpperCamelCase		)

										else:
															lowercase							=						[]
					else:
										lowercase							=						{c: []}
										lowercase							=						sub_memo

					if dn >= max_dn or c + diff >= base[k]:
										return diff, dn

					if k > ks[0]:
										while True:
															# keep doing smaller jumps
															lowercase	,						lowercase							=						next_term(__UpperCamelCase ,			k - 1 ,			i + dn ,			__UpperCamelCase		)
															diff += _diff
															dn += terms_jumped

															if dn >= max_dn or c + diff >= base[k]:
																				break
					else:
										# would be too small a jump, just compute sequential terms instead
										lowercase	,						lowercase							=						compute(__UpperCamelCase ,			__UpperCamelCase ,			i + dn ,			__UpperCamelCase		)
										diff += _diff
										dn += terms_jumped

					lowercase							=						sub_memo[c]

					# keep jumps sorted by # of terms skipped
					lowercase							=						0
					while j < len(__UpperCamelCase		):
										if jumps[j][1] > dn:
															break
										j += 1

					# cache the jump for this value digitsum(b) and c
					sub_memo[c].insert(__UpperCamelCase ,			(diff, dn, k)		)
					return (diff, dn)



def        UpperCamelCase    (							lowerCAmelCase__ ,			lowerCAmelCase__ ,			lowerCAmelCase__ ,			lowerCAmelCase__		):
					'''simple docstring'''







					if i >= n:
										return 0, i
					if k > len(__UpperCamelCase		):
										a_i.extend([0 for _ in range(k - len(__UpperCamelCase		)		)]		)

					# note: a_i -> b * 10^k + c
					# ds_b -> digitsum(b)
					# ds_c -> digitsum(c)
					lowercase							=						i
					lowercase	,						lowercase	,						lowercase							=						0, 0, 0
					for j in range(len(__UpperCamelCase		)		):
										if j >= k:
															ds_b += a_i[j]
										else:
															ds_c += a_i[j]

					while i < n:
										i += 1
										lowercase							=						ds_c + ds_b
										diff += addend
										lowercase							=						0
										for j in range(__UpperCamelCase		):
															lowercase							=						a_i[j] + addend
															lowercase	,						lowercase							=						divmod(__UpperCamelCase ,			10		)

															ds_c += a_i[j]

										if addend > 0:
															break

					if addend > 0:
										add(__UpperCamelCase ,			__UpperCamelCase ,			__UpperCamelCase		)
					return diff, i - start_i



def        UpperCamelCase    (							lowerCAmelCase__ ,			lowerCAmelCase__ ,			lowerCAmelCase__		):
					'''simple docstring'''







					for j in range(__UpperCamelCase ,			len(__UpperCamelCase		)		):
										lowercase							=						digits[j] + addend
										if s >= 10:
															lowercase	,						lowercase							=						divmod(__UpperCamelCase ,			10		)
															lowercase							=						addend // 10 + quotient
										else:
															lowercase							=						s
															lowercase							=						addend // 10

										if addend == 0:
															break

					while addend > 0:
										lowercase	,						lowercase							=						divmod(__UpperCamelCase ,			10		)
										digits.append(__UpperCamelCase		)



def        UpperCamelCase    (							lowerCAmelCase__ = 10**15		):
					'''simple docstring'''
					lowercase							=						[1]
					lowercase							=						1
					lowercase							=						0
					while True:
										lowercase	,						lowercase							=						next_term(__UpperCamelCase ,			20 ,			i + dn ,			__UpperCamelCase		)
										dn += terms_jumped
										if dn == n - i:
															break

					lowercase							=						0
					for j in range(len(__UpperCamelCase		)		):
										a_n += digits[j] * 10**j
					return a_n


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












"""simple docstring"""


import numpy as np
import torch
from torch.utils.data import DataLoader

from accelerate.utils.dataclasses import DistributedType


class 					snake_case		:


   '''simple docstring'''

   def __init__(	self :     Optional[int],       _lowerCamelCase :     Optional[int]=2,       _lowerCamelCase :     Optional[int]=3,       _lowerCamelCase :     int=64,       _lowerCamelCase :     List[str]=None  ):

     '''simple docstring'''
     __A									= np.random.default_rng(_lowerCamelCase  )
     __A									= length
     __A									= rng.normal(size=(length,)  ).astype(np.floataa  )
     __A									= a * self.x + b + rng.normal(scale=0.1,       size=(length,)  ).astype(np.floataa  )


   def __len__(	self :     str  ):

     '''simple docstring'''
     return self.length






   def __getitem__(	self :     Dict,       _lowerCamelCase :     Optional[int]  ):

     '''simple docstring'''
     return {"x": self.x[i], "y": self.y[i]}





class 					snake_case		(							torch.nn.Module						):


   '''simple docstring'''

   def __init__(	self :     Optional[Any],       _lowerCamelCase :     Tuple=0,       _lowerCamelCase :     Any=0,       _lowerCamelCase :     Optional[Any]=False  ):

     '''simple docstring'''
     super().__init__()
     __A									= torch.nn.Parameter(torch.tensor([2, 3]  ).float()  )
     __A									= torch.nn.Parameter(torch.tensor([2, 3]  ).float()  )
     __A									= True






   def 				_SCREAMING_SNAKE_CASE				(	self :     List[str],       _lowerCamelCase :     Optional[Any]=None  ):

     '''simple docstring'''
     if self.first_batch:
       print(f'Model dtype: {self.a.dtype}, {self.b.dtype}. Input dtype: {x.dtype}'  )
       __A									= False
     return x * self.a[0] + self.b[0]





class 					snake_case		(							torch.nn.Module						):


   '''simple docstring'''

   def __init__(	self :     str,       _lowerCamelCase :     Optional[Any]=0,       _lowerCamelCase :     Any=0,       _lowerCamelCase :     List[Any]=False  ):

     '''simple docstring'''
     super().__init__()
     __A									= torch.nn.Parameter(torch.tensor(_lowerCamelCase  ).float()  )
     __A									= torch.nn.Parameter(torch.tensor(_lowerCamelCase  ).float()  )
     __A									= True






   def 				_SCREAMING_SNAKE_CASE				(	self :     Optional[Any],       _lowerCamelCase :     List[str]=None  ):

     '''simple docstring'''
     if self.first_batch:
       print(f'Model dtype: {self.a.dtype}, {self.b.dtype}. Input dtype: {x.dtype}'  )
       __A									= False
     return x * self.a + self.b





def 					lowerCAmelCase				(    __UpperCamelCase		,       __UpperCamelCase = 1_6 ):




  """simple docstring"""







  from datasets import load_dataset
  from transformers import AutoTokenizer

  __A									= AutoTokenizer.from_pretrained('''bert-base-cased''' )
  __A									= {'''train''': '''tests/test_samples/MRPC/train.csv''', '''validation''': '''tests/test_samples/MRPC/dev.csv'''}
  __A									= load_dataset('''csv'''		,       data_files=__UpperCamelCase )
  __A									= datasets['''train'''].unique('''label''' )

  __A									= {v: i for i, v in enumerate(__UpperCamelCase )}

  def tokenize_function(__UpperCamelCase ):
    # max_length=None => use the model max length (it's actually the default)
    __A									= tokenizer(
        examples['''sentence1''']		,       examples['''sentence2''']		,       truncation=__UpperCamelCase		,       max_length=__UpperCamelCase		,       padding='''max_length''' )
    if "label" in examples:
      __A									= [label_to_id[l] for l in examples['''label''']]
    return outputs

  # Apply the method we just defined to all the examples in all the splits of the dataset
  __A									= datasets.map(
      __UpperCamelCase		,       batched=__UpperCamelCase		,       remove_columns=['''sentence1''', '''sentence2''', '''label''']		,       )

  def collate_fn(__UpperCamelCase ):
    # On TPU it's best to pad everything to the same length or training will be very slow.
    if accelerator.distributed_type == DistributedType.TPU:
      return tokenizer.pad(__UpperCamelCase		,       padding='''max_length'''		,       max_length=1_2_8		,       return_tensors='''pt''' )
    return tokenizer.pad(__UpperCamelCase		,       padding='''longest'''		,       return_tensors='''pt''' )

  # Instantiate dataloaders.
  __A									= DataLoader(tokenized_datasets['''train''']		,       shuffle=__UpperCamelCase		,       collate_fn=__UpperCamelCase		,       batch_size=2 )
  __A									= DataLoader(tokenized_datasets['''validation''']		,       shuffle=__UpperCamelCase		,       collate_fn=__UpperCamelCase		,       batch_size=1 )

  return train_dataloader, eval_dataloader




