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()
    {
        var N = Int64.Parse(Console.ReadLine());
        var length = Math.Sqrt(N);
        var count = 0L;
        for (long i=1;i<=length;++i)
        {
            if (N % i == 0)
            {
                long num = i - 1;
                if (num!=0 && (N % num) == (N / num)) count += num;
                num = N / i - 1;
                if (num != 0 && (N % num) == (N / num)) count += num;
            }
        }
        Console.WriteLine(count);
    }
}