#!/usr/bin/env python3

# 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?

from projecteuler import count_divisors, timing


@timing
def p012() -> None:
    i = 0
    triang = 0
    finished = 0

    # Generate all triangle numbers until the first one with more than 500 divisors is found.
    while not finished:
        i = i + 1
        triang = triang + i

        # Use the function implemented in projecteuler.py to count divisors of a number.
        if count_divisors(triang) > 500:
            finished = 1

    print('Project Euler, Problem 12')
    print(f'Answer: {triang}')


if __name__ == '__main__':
    p012()