

from __future__ import annotations

from collections import Counter



def    snake_case_(_UpperCamelCase  )							->			list[int]:



  """simple docstring"""






  _snake_case		=							[True] * n
  _snake_case		=							False
  _snake_case		=							False
  _snake_case		=							True

  for i in range(3				, int(n**0.5 + 1  )				, 2  ):
    _snake_case		=							i * 2
    while index < n:
      _snake_case		=							False
      _snake_case		=							index + i

  _snake_case		=							[2]

  for i in range(3				, _UpperCamelCase				, 2  ):
    if is_prime[i]:
      primes.append(_UpperCamelCase  )

  return primes



def    snake_case_(_UpperCamelCase  )							->			list[list[int]]:



  """simple docstring"""






  _snake_case		=							str(_UpperCamelCase  )
  _snake_case		=							[]
  _snake_case		=							['''0''', '''1''', '''2''', '''3''', '''4''', '''5''', '''6''', '''7''', '''8''', '''9''']

  for duplicate in Counter(_UpperCamelCase  ) - Counter(set(_UpperCamelCase  )  ):
    _snake_case		=							[int(number_str.replace(_UpperCamelCase				, _UpperCamelCase  )  ) for digit in digits]
    replacements.append(_UpperCamelCase  )

  return replacements



def    snake_case_(_UpperCamelCase = 8  )							->			int:



  """simple docstring"""






  _snake_case		=							set()

  # Filter primes with less than 3 replaceable digits
  _snake_case		=							{
      x for x in set(prime_sieve(1_000_000  )  ) if len(str(_UpperCamelCase  )  ) - len(set(str(_UpperCamelCase  )  )  ) >= 3
  }

  for prime in primes:
    if prime in numbers_checked:
      continue

    _snake_case		=							digit_replacements(_UpperCamelCase  )

    for family in replacements:
      numbers_checked.update(_UpperCamelCase  )
      _snake_case		=							primes.intersection(_UpperCamelCase  )

      if len(_UpperCamelCase  ) != family_length:
        continue

      return min(_UpperCamelCase  )

  return -1


if __name__ == "__main__":
 print(solution())




import numpy as np



def    snake_case_(_UpperCamelCase  )							->			Any:



  """simple docstring"""






  _snake_case		=							np.exp(_UpperCamelCase  )

  # Add up the all the exponentials
  _snake_case		=							np.sum(_UpperCamelCase  )

  # Divide every exponent by the sum of all exponents
  _snake_case		=							exponent_vector / sum_of_exponents

  return softmax_vector


if __name__ == "__main__":
 print(softmax((0,)))

