
'''simple docstring'''
from itertools import product

def     UpperCamelCase_  (						__SCREAMING_SNAKE_CASE = 1_5							):
    """simple docstring"""






    snake_case_			:     float        =    0.0
    snake_case_			:     float
    snake_case_			:     int
    snake_case_			:     int
    snake_case_			:     int
    snake_case_			:     int
    snake_case_			:     tuple[int, ...]

    for series in product(range(2							),		repeat=__SCREAMING_SNAKE_CASE							):
        snake_case_			:     Optional[Any]        =    series.count(1							)
        snake_case_			:     Any        =    num_turns - num_blue
        if num_red >= num_blue:
            continue
        snake_case_			:     Optional[Any]        =    1.0
        for ind, col in enumerate(__SCREAMING_SNAKE_CASE,		2							):
            if col == 0:
                prob *= (ind - 1) / ind
            else:
                prob *= 1 / ind

        total_prob += prob

    return int(1 / total_prob							)


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






'''simple docstring'''
import itertools

def     UpperCamelCase_  (						__SCREAMING_SNAKE_CASE = 1_0_0_0_0_0_0							):
    """simple docstring"""






    snake_case_			:     Optional[int]        =    [1]

    for i in itertools.count(len(__SCREAMING_SNAKE_CASE							)							):
        snake_case_			:     str        =    0
        for j in itertools.count(1							):
            snake_case_			:     List[str]        =    -1 if j % 2 == 0 else +1
            snake_case_			:     str        =    (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() = }""")




