





from itertools import product
def 			__UpperCamelCase				(			lowercase__	:       int = 15		)	->      int:
    '''simple docstring'''





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

    for series in product(range(2		)		,    repeat=lowercase__		):
        lowerCAmelCase_					:	str						=   series.count(1		)
        lowerCAmelCase_					:	Optional[int]						=   num_turns - num_blue
        if num_red >= num_blue:
            continue
        lowerCAmelCase_					:	Any						=   1.0
        for ind, col in enumerate(lowercase__		,    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() = }""")









from __future__ import annotations

import math
from itertools import permutations
def 			__UpperCamelCase				(			lowercase__	:       int		)	->      bool:
    '''simple docstring'''





    if 1 < number < 4:
        # 2 and 3 are primes
        return True
    elif number < 2 or number % 2 == 0 or number % 3 == 0:
        # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
        return False

    # All primes number are in format of 6k +/- 1
    for i in range(5		,    int(math.sqrt(lowercase__		) + 1		)		,    6		):
        if number % i == 0 or number % (i + 2) == 0:
            return False
    return True
def 			__UpperCamelCase				(			lowercase__	:       int = 7		)	->      int:
    '''simple docstring'''





    lowerCAmelCase_					:	str						=   """""".join(str(lowercase__		) for i in range(1		,    n + 1		)		)
    lowerCAmelCase_					:	Any						=   [int("""""".join(lowercase__		)		) for i in permutations(lowercase__		,    lowercase__		)]
    lowerCAmelCase_					:	List[Any]						=   [num for num in perm_list if is_prime(lowercase__		)]
    return max(lowercase__		) if pandigitals else 0


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


