
'''simple docstring'''





import numpy as np





def 							snake_case				(		UpperCAmelCase						)->      List[Any]:







      """simple docstring"""
      __A													=      np.exp(UpperCAmelCase						)

      # Add up the all the exponentials
      __A													=      np.sum(UpperCAmelCase						)

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

      return softmax_vector


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







'''simple docstring'''

from __future__ import annotations

_lowerCamelCase :				Optional[int]														= """Alexander Joslin"""



def  _lowerCAmelCase				(				__a      )  ->      int:
     '''simple docstring'''







     if number <= 0:
          _UpperCamelCase  :Optional[Any]       =F'''n must be greater than 0. Got n = {number}'''
          raise ValueError(__a      )

     _UpperCamelCase  :Optional[Any]       =[number + 1] * (number + 1)

     # starting position
     _UpperCamelCase  :int       =0
     for i in range(1			,      __a      ):
          _UpperCamelCase  :List[str]       =min(table[i + 1]			,      table[i] + 1      )
          # check if out of bounds
          if i * 2 <= number:
               _UpperCamelCase  :int       =min(table[i * 2]			,      table[i] + 1      )
          # check if out of bounds
          if i * 3 <= number:
               _UpperCamelCase  :Tuple       =min(table[i * 3]			,      table[i] + 1      )
     return table[number]


if __name__ == "__main__":
      import doctest

      doctest.testmod()