

from itertools import product

def 	__snake_case		(      __UpperCamelCase     :      int							,__UpperCamelCase     :      int  ):



      """simple docstring"""

      A_		   =							sides_number
      A_		   =							max_face_number * dice_number
      A_		   =							[0] * (max_total + 1)

      A_		   =							1
      A_		   =							range(__lowercase							,max_face_number + 1  )
      for dice_numbers in product(__lowercase							,repeat=__lowercase  ):
            A_		   =							sum(__lowercase  )
            totals_frequencies[total] += 1

      return totals_frequencies

def 	__snake_case		(      ):



      """simple docstring"""

      A_		   =							total_frequency_distribution(
          sides_number=4							,dice_number=9  )
      A_		   =							total_frequency_distribution(
          sides_number=6							,dice_number=6  )

      A_		   =							0
      A_		   =							9
      A_		   =							4 * 9
      A_		   =							6
      for peter_total in range(__lowercase							,max_peter_total + 1  ):
            peter_wins_count += peter_totals_frequencies[peter_total] * sum(
                colin_totals_frequencies[min_colin_total:peter_total]  )

      A_		   =							(4**9) * (6**6)
      A_		   =							peter_wins_count / total_games_number

      A_		   =							round(__lowercase							,ndigits=7  )

      return rounded_peter_win_probability


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






'''simple docstring'''




import string
from math import logaa
def 	UpperCAmelCase_							(					__lowercase							:      str			,     __lowercase							:      str       )		->       int:


     '''simple docstring'''



     _UpperCAmelCase     							=   document.translate(
         str.maketrans(""			,     ""			,     string.punctuation       )       ).replace("\n"			,     ""       )
     _UpperCAmelCase     							=   document_without_punctuation.split(" "       )  # word tokenization
     return len([word for word in tokenize_document if word.lower() == term.lower()]       )
def 	UpperCAmelCase_							(					__lowercase							:      str			,     __lowercase							:      str       )		->       tuple[int, int]:


     '''simple docstring'''



     _UpperCAmelCase     							=   corpus.lower().translate(
         str.maketrans(""			,     ""			,     string.punctuation       )       )  # strip all punctuation and replace it with ''
     _UpperCAmelCase     							=   corpus_without_punctuation.split("\n"       )
     _UpperCAmelCase     							=   term.lower()
     return (len([doc for doc in docs if term in doc]       ), len(__lowercase       ))
def 	UpperCAmelCase_							(					__lowercase							:      int			,     __lowercase							:      int			,     __lowercase							:      Union[str, Any]=False       )		->       float:


     '''simple docstring'''



     if smoothing:
          if n == 0:
               raise ValueError("log10(0) is undefined."       )
          return round(1 + logaa(n / (1 + df)       )			,     3       )

     if df == 0:
          raise ZeroDivisionError("df must be > 0"       )
     elif n == 0:
          raise ValueError("log10(0) is undefined."       )
     return round(logaa(n / df       )			,     3       )






def 	UpperCAmelCase_							(					__lowercase							:      int			,     __lowercase							:      int       )		->       float:


     '''simple docstring'''



     return round(tf * idf			,     3       )




