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.Linq;
using System.Collections.Generic;

class Program
{
    static void Main(string[] args)
    {
        var N = long.Parse(Console.ReadLine());
        var max = Math.Sqrt(N);
        var sum = 0L;
        // N = m * r + r = r(m+1)
        // r <= m であることに注意する
        for (long r = (long)max; r >= 1; r--)
        {
            if (N % r != 0) continue;

            var A = N / r;
            var m = A - 1;
            if (r < m)
                sum += m;
        }

        Console.WriteLine(sum);
    }
}