"""
It can be seen that the number, 125874, and its double, 251748,
contain exactly the same digits, but in a different order.

Find the smallest positive integer, x, such that
2x, 3x, 4x, 5x, and 6x contain the same digits.
"""

import time


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

    return wrapper


def has_same_digits(x, y):
    return sorted(str(x)) == sorted(str(y))


def signature(n):
    count = [0] * 10
    while n:
        count[n % 10] += 1
        n //= 10
    return tuple(count)


def find_smallest_permuted_multiple():
    x = 1
    while True:
        if not x % 9 == 0:
            x += 1
            continue
        for i in range(2, 7):
            if not has_same_digits(x, x * i):
                break
        else:
            return x
        x += 1


def better_permuted_multiple():
    n = 1
    while True:
        start = 10 ** (n - 1)
        # 核心约束：x * 6 必须仍是n位数
        end = int(10**n / 6) + 1

        # 步长为9：利用模9同余原理
        for x in range((start + 8) // 9 * 9, end, 9):
            sig = signature(x)
            # 检查2x到6x是否共享相同签名
            if all(signature(k * x) == sig for k in range(2, 7)):
                return x
        n += 1


@timer
def main():
    result = find_smallest_permuted_multiple()
    print(f"{result}")


@timer
def main_better():
    result = better_permuted_multiple()
    print(f"{result}")


if __name__ == "__main__":
    main()
    main_better()