



'''simple docstring'''


import math

from numpy import inf
from scipy.integrate import quad






def  UpperCAmelCase_       (		lowercase__       ):


     '''simple docstring'''







     if num <= 0:
          raise ValueError("math domain error"       )

     return quad(lowercase__       ,	0       ,	lowercase__       ,	args=(lowercase__)       )[0]






def  UpperCAmelCase_       (		lowercase__       ,	lowercase__       ):


     '''simple docstring'''







     return math.pow(lowercase__       ,	z - 1       ) * math.exp(-x       )


if __name__ == "__main__":
  from doctest import testmod

  testmod()







'''simple docstring'''


from __future__ import annotations






def  UpperCAmelCase_       (		lowercase__       ):


     '''simple docstring'''







     a_       		=str(lowercase__       )
     return len(lowercase__       ) == 9 and set(lowercase__       ) == set("123456789"       )






def  UpperCAmelCase_       (		):


     '''simple docstring'''







     for base_num in range(9_9_9_9       ,	4_9_9_9       ,	-1       ):
          a_       		=1_0_0_0_0_2 * base_num
          if is_9_pandigital(lowercase__       ):
               return candidate

     for base_num in range(3_3_3       ,	9_9       ,	-1       ):
          a_       		=1_0_0_2_0_0_3 * base_num
          if is_9_pandigital(lowercase__       ):
               return candidate

     return None


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


