"""
A palindromic number reads the same both ways.
The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99.
Find the largest palindrome made from the product of two 3-digit numbers.
"""


def is_palindrome(n: int) -> bool:
    return str(n) == str(n)[::-1]


def initial_idea() -> None:
    a = 999
    b = 999
    y = (0, 0)
    max_palindrome = 0
    for i in range(a, 99, -1):
        for j in range(b, 99, -1):
            product = i * j
            if is_palindrome(product) and product > max_palindrome:
                max_palindrome = product
                y = (i, j)
    print(f"{max_palindrome} = {y[0]} × {y[1]}")


def largest_palindrome_product():
    max_palindrome = 0
    max_factors = (0, 0)

    # 外层循环从大到小，且只遍历11的倍数
    for i in range(990, 100, -11):  # 从990开始（最大的11的倍数）
        # 内层循环从i开始（避免重复，利用乘法交换律）
        for j in range(999, i - 1, -1):
            product = i * j

            # 提前终止：如果乘积已小于当前最大值
            if product <= max_palindrome:
                break

            # 检查是否为回文数
            if str(product) == str(product)[::-1]:
                max_palindrome = product
                max_factors = (i, j)
                break  # 找到即可跳出内层循环

    return max_palindrome, max_factors


if __name__ == "__main__":
    initial_idea()
    x, y = largest_palindrome_product()
    print(f"{x} = {y[0]} × {y[1]}")