"""
The number 3797 has an interesting property.
Being prime itself, it is possible to continuously remove digits from left to right,
and remain prime at each stage: 3797, 797, 97, and 7.
Similarly we can work from right to left: 3797, 379, 37, and 3.

Find the sum of the only eleven primes that are both truncatable from left to right and right to left.

NOTE: 2, 3, 5, and 7 are not considered to be truncatable primes.
"""

import time
from itertools import product


def timer(func):
    def wrapper(*args, **kwargs):
        start_time = time.time()
        result = func(*args, **kwargs)
        end_time = time.time()
        print(f"Time taken: {end_time - start_time:.6f} seconds")
        return result

    return wrapper


def combine_lists(a: list[int], b: list[int | None], c: list[int]) -> list[int]:
    """将三个列表的每个元素组合成数字"""
    return [int(f"{x}{y}{z}") for x, y, z in product(a, b, c)]


def is_prime(n: int) -> bool:
    """判断一个数是否为素数"""
    if n < 2:
        return False
    for i in range(2, int(n**0.5) + 1):
        if n % i == 0:
            return False
    return True


def truncate_left(n: int) -> bool:
    """从左到右截断一个数"""
    length = len(str(n))
    while n > 0:
        if not is_prime(n):
            return False
        n %= 10 ** (length - 1)
        length -= 1
    return True


def truncate_right(n: int) -> bool:
    """从右到左截断一个数"""
    while n > 0:
        if not is_prime(n):
            return False
        n //= 10
    return True


def TruncatablePrime() -> list[int]:
    begin = [2, 3, 5, 7]
    end = [3, 7]
    middle = [1, 3, 7, 9]
    res = []
    for length in range(2, 7):
        if length - 2 == 0:
            midb = []
        else:
            midb = product(middle, repeat=length - 2)
            midb = [int("".join(map(str, x))) for x in midb]
        nums = combine_lists(begin, midb, end)
        for num in nums:
            if is_prime(num):
                if truncate_left(num) and truncate_right(num):
                    res.append(num)
    return res


@timer
def main():
    print(sum(TruncatablePrime()))


if __name__ == "__main__":
    main()