Problem:
Score : 500 points

Problem Statement

Snuke received a positive integer N from Takahashi.
A positive integer m is called a favorite number when the following condition is satisfied:

The quotient and remainder of N divided by m are equal, that is, \lfloor \frac{N}{m} \rfloor = N \bmod m holds.

Find all favorite numbers and print the sum of those.

Constraints

All values in input are integers.

1 \leq N \leq 10^{12}

Input

Input is given from Standard Input in the following format:

N

Output

Print the answer.

Sample Input 1

8

Sample Output 1

10

There are two favorite numbers: 3 and 7. Print the sum of these, 10.

Sample Input 2

1000000000000

Sample Output 2

2499686339916

Watch out for overflow.

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Math;

class Program
{
    static void Main()
    {
        var N = long.Parse(ReadLine());

        var d = yakusuu(N);
        var ans = 0L;
        for (int i = 0; i < d.Length; i++)
        {
            var k = (N - d[i]) / d[i];
            if (k != 0 && N / k == N % k) ans += k;
        }

        WriteLine(ans);
    }

    static long[] yakusuu(long n)
    {
        var r = new List<long>();
        for (long i = 1; i * i <= n; i++)
        {
            if (n % i == 0)
            {
                r.Add(i);
                if (i * i != n) r.Add(n / i);
            }
        }
        return r.ToArray();
    }
}