
from math import sqrt




def        __UpperCamelCase					(    lowerCAmelCase__							:    int  ):
 assert isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  ) and (
     number >= 0
 ), "'number' must been an int and positive"

 __a			:  Tuple		    =  True

 # 0 and 1 are none primes.
 if number <= 1:
  __a			:  Dict		    =  False

 for divisor in range(2  ,       int(round(sqrt(_UpperCAmelCase  )  )  ) + 1  ):
  # if 'number' divisible by 'divisor' then sets 'status'
  # of false and break up the loop.
  if number % divisor == 0:
   __a			:  str		    =  False
   break

    # precondition
 assert isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  ), "'status' must been from type bool"

 return status




def        __UpperCamelCase					(    lowerCAmelCase__							:    Optional[int]  ):
 assert isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  ) and (n > 2), "'N' must been an int and > 2"

 # beginList: contains all natural numbers from 2 up to N
 __a			:  Union[str, Any]		    =  list(range(2  ,       n + 1  )  )

 __a			:  Tuple		    =  []  # this list will be returns.

 # actual sieve of erathostenes
 for i in range(len(_UpperCAmelCase  )  ):
  for j in range(i + 1  ,       len(_UpperCAmelCase  )  ):
   if (begin_list[i] != 0) and (begin_list[j] % begin_list[i] == 0):
    __a			:  Dict		    =  0

    # filters actual prime numbers.
 __a			:  Optional[Any]		    =  [x for x in begin_list if x != 0]

 # precondition
 assert isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  ), "'ans' must been from type list"

 return ans




def        __UpperCamelCase					(    lowerCAmelCase__							:    Optional[Any]  ):
 assert isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  ) and (n > 2), "'N' must been an int and > 2"

 __a			:  Union[str, Any]		    =  []

 # iterates over all numbers between 2 up to N+1
 # if a number is prime then appends to list 'ans'
 for number in range(2  ,       n + 1  ):
  if is_prime(_UpperCAmelCase  ):
   ans.append(_UpperCAmelCase  )

    # precondition
 assert isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  ), "'ans' must been from type list"

 return ans




def        __UpperCamelCase					(    lowerCAmelCase__							:    Any  ):
 assert isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  ) and number >= 0, "'number' must been an int and >= 0"

 __a			:  Any		    =  []  # this list will be returns of the function.

 # potential prime number factors.

 __a			:  Any		    =  2

 __a			:  Union[str, Any]		    =  number

 if number == 0 or number == 1:
  ans.append(_UpperCAmelCase  )

 # if 'number' not prime then builds the prime factorization of 'number'
 elif not is_prime(_UpperCAmelCase  ):
  while quotient != 1:
   if is_prime(_UpperCAmelCase  ) and (quotient % factor == 0):
    ans.append(_UpperCAmelCase  )
    quotient /= factor
   else:
    factor += 1

 else:
  ans.append(_UpperCAmelCase  )

 # precondition
 assert isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  ), "'ans' must been from type list"

 return ans




def        __UpperCamelCase					(    lowerCAmelCase__							:    Union[str, Any]  ):
 assert isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  ) and (
     number >= 0
 ), "'number' bust been an int and >= 0"

 __a			:  Optional[Any]		    =  0

 # prime factorization of 'number'
 __a			:  Dict		    =  prime_factorization(_UpperCAmelCase  )

 __a			:  Union[str, Any]		    =  max(_UpperCAmelCase  )

 # precondition
 assert isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  ), "'ans' must been from type int"

 return ans




def        __UpperCamelCase					(    lowerCAmelCase__							:    List[Any]  ):
 assert isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  ) and (
     number >= 0
 ), "'number' bust been an int and >= 0"

 __a			:  List[str]		    =  0

 # prime factorization of 'number'
 __a			:  int		    =  prime_factorization(_UpperCAmelCase  )

 __a			:  int		    =  min(_UpperCAmelCase  )

 # precondition
 assert isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  ), "'ans' must been from type int"

 return ans




def        __UpperCamelCase					(    lowerCAmelCase__							:    List[str]  ):
 assert isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  ), "'number' must been an int"
 assert isinstance(number % 2 == 0  ,       _UpperCAmelCase  ), "compare bust been from type bool"

 return number % 2 == 0




def        __UpperCamelCase					(    lowerCAmelCase__							:    str  ):
 assert isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  ), "'number' must been an int"
 assert isinstance(number % 2 != 0  ,       _UpperCAmelCase  ), "compare bust been from type bool"

 return number % 2 != 0




def        __UpperCamelCase					(    lowerCAmelCase__							:    Tuple  ):
 assert (
     isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  ) and (number > 2) and is_even(_UpperCAmelCase  )
 ), "'number' must been an int, even and > 2"

 __a			:  Optional[Any]		    =  []  # this list will returned

 # creates a list of prime numbers between 2 up to 'number'
 __a			:  List[str]		    =  get_prime_numbers(_UpperCAmelCase  )
 __a			:  Optional[Any]		    =  len(_UpperCAmelCase  )

 # run variable for while-loops.
 __a			:  Any		    =  0
 __a			:  Tuple		    =  None

 # exit variable. for break up the loops
 __a			:  Optional[int]		    =  True

 while i < len_pn and loop:
  __a			:  Union[str, Any]		    =  i + 1

  while j < len_pn and loop:
   if prime_numbers[i] + prime_numbers[j] == number:
    __a			:  Optional[int]		    =  False
    ans.append(prime_numbers[i]  )
    ans.append(prime_numbers[j]  )

   j += 1

  i += 1

 # precondition
 assert (
     isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  )
     and (len(_UpperCAmelCase  ) == 2)
     and (ans[0] + ans[1] == number)
     and is_prime(ans[0]  )
     and is_prime(ans[1]  )
 ), "'ans' must contains two primes. And sum of elements must been eq 'number'"

 return ans




def        __UpperCamelCase					(    lowerCAmelCase__							:    str  ,       lowerCAmelCase__							:    List[Any]  ):
 assert (
     isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  )
     and isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  )
     and (numbera >= 0)
     and (numbera >= 0)
 ), "'number1' and 'number2' must been positive integer."

 __a			:  Optional[Any]		    =  0

 while numbera != 0:
  __a			:  Tuple		    =  numbera % numbera
  __a			:  Any		    =  numbera
  __a			:  Tuple		    =  rest

 # precondition
 assert isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  ) and (
     numbera >= 0
 ), "'number' must been from type int and positive"

 return numbera




def        __UpperCamelCase					(    lowerCAmelCase__							:    Any  ,       lowerCAmelCase__							:    List[str]  ):
 assert (
     isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  )
     and isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  )
     and (numbera >= 1)
     and (numbera >= 1)
 ), "'number1' and 'number2' must been positive integer."

 __a			:  Any		    =  1  # actual answer that will be return.

 # for kgV (x,1)
 if numbera > 1 and numbera > 1:
  # builds the prime factorization of 'number1' and 'number2'
  __a			:  Optional[int]		    =  prime_factorization(_UpperCAmelCase  )
  __a			:  Dict		    =  prime_factorization(_UpperCAmelCase  )

 elif numbera == 1 or numbera == 1:
  __a			:  Union[str, Any]		    =  []
  __a			:  Union[str, Any]		    =  []
  __a			:  List[str]		    =  max(_UpperCAmelCase  ,       _UpperCAmelCase  )

 __a			:  Union[str, Any]		    =  0
 __a			:  str		    =  0

 __a			:  Optional[int]		    =  []  # captured numbers int both 'primeFac1' and 'primeFac2'

 # iterates through primeFac1
 for n in prime_fac_a:
  if n not in done:
   if n in prime_fac_a:
    __a			:  Optional[Any]		    =  prime_fac_a.count(_UpperCAmelCase  )
    __a			:  Optional[int]		    =  prime_fac_a.count(_UpperCAmelCase  )

    for _ in range(max(_UpperCAmelCase  ,       _UpperCAmelCase  )  ):
     ans *= n

   else:
    __a			:  List[str]		    =  prime_fac_a.count(_UpperCAmelCase  )

    for _ in range(_UpperCAmelCase  ):
     ans *= n

   done.append(_UpperCAmelCase  )

    # iterates through primeFac2
 for n in prime_fac_a:
  if n not in done:
   __a			:  List[Any]		    =  prime_fac_a.count(_UpperCAmelCase  )

   for _ in range(_UpperCAmelCase  ):
    ans *= n

   done.append(_UpperCAmelCase  )

    # precondition
 assert isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  ) and (
     ans >= 0
 ), "'ans' must been from type int and positive"

 return ans




def        __UpperCamelCase					(    lowerCAmelCase__							:    Tuple  ):
 assert isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  ) and (n >= 0), "'number' must been a positive int"

 __a			:  int		    =  0
 __a			:  Tuple		    =  2  # this variable holds the answer

 while index < n:
  index += 1

  ans += 1  # counts to the next number

  # if ans not prime then
  # runs to the next prime number.
  while not is_prime(_UpperCAmelCase  ):
   ans += 1

    # precondition
 assert isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  ) and is_prime(
     _UpperCAmelCase  ), "'ans' must been a prime number and from type int"

 return ans




def        __UpperCamelCase					(    lowerCAmelCase__							:    str  ,       lowerCAmelCase__							:    List[Any]  ):
 assert (
     is_prime(_UpperCAmelCase  ) and is_prime(_UpperCAmelCase  ) and (p_number_a < p_number_a)
 ), "The arguments must been prime numbers and 'pNumber1' < 'pNumber2'"

 __a			:  Any		    =  p_number_a + 1  # jump to the next number

 __a			:  List[Any]		    =  []  # this list will be returns.

 # if number is not prime then
 # fetch the next prime number.
 while not is_prime(_UpperCAmelCase  ):
  number += 1

 while number < p_number_a:
  ans.append(_UpperCAmelCase  )

  number += 1

  # fetch the next prime number.
  while not is_prime(_UpperCAmelCase  ):
   number += 1

    # precondition
 assert (
     isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  )
     and ans[0] != p_number_a
     and ans[len(_UpperCAmelCase  ) - 1] != p_number_a
 ), "'ans' must been a list without the arguments"

 # 'ans' contains not 'pNumber1' and 'pNumber2' !
 return ans




def        __UpperCamelCase					(    lowerCAmelCase__							:    Any  ):
 assert isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  ) and (n >= 1), "'n' must been int and >= 1"

 __a			:  Union[str, Any]		    =  []  # will be returned.

 for divisor in range(1  ,       n + 1  ):
  if n % divisor == 0:
   ans.append(_UpperCAmelCase  )

    # precondition
 assert ans[0] == 1 and ans[len(_UpperCAmelCase  ) - 1] == n, "Error in function getDivisiors(...)"

 return ans




def        __UpperCamelCase					(    lowerCAmelCase__							:    List[Any]  ):
 assert isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  ) and (
     number > 1
 ), "'number' must been an int and >= 1"

 __a			:  Tuple		    =  get_divisors(_UpperCAmelCase  )

 # precondition
 assert (
     isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  )
     and (divisors[0] == 1)
     and (divisors[len(_UpperCAmelCase  ) - 1] == number)
 ), "Error in help-function getDivisiors(...)"

 # summed all divisors up to 'number' (exclusive), hence [:-1]
 return sum(divisors[:-1]  ) == number




def        __UpperCamelCase					(    lowerCAmelCase__							:    List[Any]  ,       lowerCAmelCase__							:    List[str]  ):
 assert (
     isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  )
     and isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  )
     and (denominator != 0)
 ), "The arguments must been from type int and 'denominator' != 0"

 # build the greatest common divisor of numerator and denominator.
 __a			:  Optional[int]		    =  gcd(abs(_UpperCAmelCase  )  ,       abs(_UpperCAmelCase  )  )

 # precondition
 assert (
     isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  )
     and (numerator % gcd_of_fraction == 0)
     and (denominator % gcd_of_fraction == 0)
 ), "Error in function gcd(...,...)"

 return (numerator // gcd_of_fraction, denominator // gcd_of_fraction)




def        __UpperCamelCase					(    lowerCAmelCase__							:    int  ):
 assert isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  ) and (n >= 0), "'n' must been a int and >= 0"

 __a			:  List[str]		    =  1  # this will be return.

 for factor in range(1  ,       n + 1  ):
  ans *= factor

 return ans




def        __UpperCamelCase					(    lowerCAmelCase__							:    str  ):
 assert isinstance(_UpperCAmelCase  ,       _UpperCAmelCase  ) and (n >= 0), "'n' must been an int and >= 0"

 __a			:  int		    =  0
 __a			:  List[str]		    =  1
 __a			:  Optional[Any]		    =  1  # this will be return

 for _ in range(n - 1  ):
  __a			:  Dict		    =  ans
  ans += fiba
  __a			:  Dict		    =  tmp

 return ans


import unicodedata
from dataclasses import dataclass
from typing import Optional, Union

import numpy as np

from transformers.data.data_collator import DataCollatorMixin
from transformers.file_utils import PaddingStrategy
from transformers.tokenization_utils_base import PreTrainedTokenizerBase




def        __UpperCamelCase					(    lowerCAmelCase__							:    Union[str, Any]  ,       lowerCAmelCase__							:    int  ,       lowerCAmelCase__							:    List[str]  ,       lowerCAmelCase__							:    Any  ):
 if isinstance(lowerCAmelCase__  ,       lowerCAmelCase__  ):
  __a			:  Union[str, Any]		    =  np.full((len(lowerCAmelCase__  ), sequence_length, 2)  ,       lowerCAmelCase__  )
 else:
  __a			:  str		    =  np.full((len(lowerCAmelCase__  ), sequence_length)  ,       lowerCAmelCase__  )

 for i, tensor in enumerate(lowerCAmelCase__  ):
  if padding_side == "right":
   if isinstance(lowerCAmelCase__  ,       lowerCAmelCase__  ):
    __a			:  Any		    =  tensor[:sequence_length]
   else:
    __a			:  List[Any]		    =  tensor[:sequence_length]
  else:
   if isinstance(lowerCAmelCase__  ,       lowerCAmelCase__  ):
    __a			:  Dict		    =  tensor[:sequence_length]
   else:
    __a			:  int		    =  tensor[:sequence_length]

 return out_tensor.tolist()




def        __UpperCamelCase					(    lowerCAmelCase__							:    Optional[Any]  ):
 __a			:  str		    =  ord(lowerCAmelCase__  )
 if (cp >= 3_3 and cp <= 4_7) or (cp >= 5_8 and cp <= 6_4) or (cp >= 9_1 and cp <= 9_6) or (cp >= 1_2_3 and cp <= 1_2_6):
  return True
 __a			:  List[str]		    =  unicodedata.category(lowerCAmelCase__  )
 if cat.startswith('''P'''  ):
  return True
 return False



@dataclass
class 		UpperCamelCase__  (	__lowercase   ):
   _SCREAMING_SNAKE_CASE				:							PreTrainedTokenizerBase
   _SCREAMING_SNAKE_CASE				:							Union[bool, str, PaddingStrategy]     	=				True
   _SCREAMING_SNAKE_CASE				:							Optional[int]     	=				None
   _SCREAMING_SNAKE_CASE				:							Optional[int]     	=				None
   _SCREAMING_SNAKE_CASE				:							int     	=				-100
   _SCREAMING_SNAKE_CASE				:							str     	=				"pt"
   def 				lowerCAmelCase      (self			: str ,    snake_case_			: Tuple       ):
    import torch

    __a			:  Union[str, Any]		    =  '''label''' if '''label''' in features[0].keys() else '''labels'''
    __a			:  Tuple		    =  [feature[label_name] for feature in features] if label_name in features[0].keys() else None
    __a			:  Union[str, Any]		    =  self.tokenizer.pad(
        snake_case_ ,    padding=self.padding ,    max_length=self.max_length ,    pad_to_multiple_of=self.pad_to_multiple_of ,    return_tensors='''pt''' if labels is None else None ,    )

    if labels is None:
     return batch

    __a			:  List[str]		    =  torch.tensor(batch['''entity_ids''']       ).shape[1]
    __a			:  Tuple		    =  self.tokenizer.padding_side
    if padding_side == "right":
     __a			:  Union[str, Any]		    =  [
         list(snake_case_       ) + [self.label_pad_token_id] * (sequence_length - len(snake_case_       )) for label in labels
     ]
    else:
     __a			:  Dict		    =  [
         [self.label_pad_token_id] * (sequence_length - len(snake_case_       )) + list(snake_case_       ) for label in labels
     ]

    __a			:  Dict		    =  [feature['''ner_tags'''] for feature in features]
    __a			:  Optional[Any]		    =  padding_tensor(snake_case_ ,    -1 ,    snake_case_ ,    snake_case_       )
    __a			:  Union[str, Any]		    =  [feature['''original_entity_spans'''] for feature in features]
    __a			:  Optional[int]		    =  padding_tensor(snake_case_ ,    (-1, -1) ,    snake_case_ ,    snake_case_       )
    __a			:  List[str]		    =  {k: torch.tensor(snake_case_ ,    dtype=torch.intaa       ) for k, v in batch.items()}

    return batch
