


import itertools

def       _a	(					SCREAMING_SNAKE_CASE						:					int = 1000000  ):







 """simple docstring"""



 UpperCamelCase__       :     List[str] 							= [1]

 for i in itertools.count(len(SCREAMING_SNAKE_CASE  )  ):
  UpperCamelCase__       :     Optional[int] 							= 0
  for j in itertools.count(1  ):
   UpperCamelCase__       :     List[str] 							= -1 if j % 2 == 0 else +1
   UpperCamelCase__       :     Any 							= (j * j * 3 - j) // 2
   if index > i:
    break
   item += partitions[i - index] * sign
   item %= number
   index += j
   if index > i:
    break
   item += partitions[i - index] * sign
   item %= number

  if item == 0:
   return i
  partitions.append(SCREAMING_SNAKE_CASE  )

 return 0


if __name__ == "__main__":
       import doctest

       doctest.testmod()

       print(f"{solution() = }")






import numpy as np

def       _a	(					SCREAMING_SNAKE_CASE						:					Tuple  ):







 """simple docstring"""



 UpperCamelCase__       :     str 							= np.exp(SCREAMING_SNAKE_CASE  )

 # Add up the all the exponentials
 UpperCamelCase__       :     Optional[int] 							= np.sum(SCREAMING_SNAKE_CASE  )

 # Divide every exponent by the sum of all exponents
 UpperCamelCase__       :     Optional[Any] 							= exponent_vector / sum_of_exponents

 return softmax_vector


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


