"""
The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number
would be 1+2+3+4+5+6+7=28. The first ten terms would be:

    1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

Let us list the factors of the first seven triangle numbers:

1 : 1
3 : 1, 3
6 : 1, 2, 3, 6
10 : 1, 2, 5, 10
15 : 1, 3, 5, 15
21 : 1, 3, 7, 21
28 : 1, 2, 4, 7, 14, 28

We can see that 28 is the first triangle number to have over five divisors.
What is the value of the first triangle number to have over five hundred divisors?

NOTE：

-> in Math
    解法的核心是找到所有质因数及对应的最大幂, 根据组合数学的方法估算因数数量
-> in Coding
    循环遍历
"""

import math
import time


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} seconds")
        return result

    return wrapper


def get_factors(n):
    if n == 0:
        raise ValueError("0 没有因数集合")
    n = abs(n)  # 处理负数
    factors = set()
    for i in range(1, int(math.isqrt(n)) + 1):
        if n % i == 0:
            factors.add(i)
            factors.add(n // i)
    return sorted(factors)


def get_triangle_number(n: int) -> int:
    return n * (n + 1) // 2


@timer
def main_coding() -> None:
    n = 1
    while True:
        triangle_number = get_triangle_number(n)
        factors = get_factors(triangle_number)
        if len(factors) > 500:
            print(triangle_number)
            break
        n += 1


if __name__ == "__main__":
    main_coding()