
from itertools import product





def 	SCREAMING_SNAKE_CASE__    (      __lowerCAmelCase    ,		__lowerCAmelCase							):
    snake_case__						=				sides_number
    snake_case__						=				max_face_number * dice_number
    snake_case__						=				[0] * (max_total + 1)

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

    return totals_frequencies





def 	SCREAMING_SNAKE_CASE__    (      ):
    snake_case__						=				total_frequency_distribution(
        sides_number=4    ,		dice_number=9							)
    snake_case__						=				total_frequency_distribution(
        sides_number=6    ,		dice_number=6							)

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

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

    snake_case__						=				round(__lowerCAmelCase    ,		ndigits=7							)

    return rounded_peter_win_probability


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





from __future__ import annotations





def 	SCREAMING_SNAKE_CASE__    (      __lowerCAmelCase    ,		__lowerCAmelCase							):
    if len(__lowerCAmelCase							) == 0:
        return False
    snake_case__						=				len(__lowerCAmelCase							) // 2
    if a_list[midpoint] == item:
        return True
    if item < a_list[midpoint]:
        return binary_search(a_list[:midpoint]    ,		__lowerCAmelCase							)
    else:
        return binary_search(a_list[midpoint + 1 :]    ,		__lowerCAmelCase							)


if __name__ == "__main__":
     __magic_name__            =  input('''Enter numbers separated by comma:\n''').strip()
     __magic_name__            =  [int(item.strip()) for item in user_input.split(''',''')]
     __magic_name__            =  int(input('''Enter the number to be found in the list:\n''').strip())
     __magic_name__            =  '''''' if binary_search(sequence, target) else '''not '''
     print(F'''{target} was {not_str}found in {sequence}''')



