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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.IOException;
import java.util.HashSet;
import java.util.Scanner;
import java.util.TreeSet;

public class Main {
	
	public static void main(String[] args) throws NumberFormatException, IOException
	{
		new Main().run();
	}
	
	public void run() throws NumberFormatException, IOException
	{
		Scanner file = new Scanner(System.in);
		long N = file.nextLong();
		HashSet<Long> factors = new HashSet<Long>();
		for(long i = 2;i*i<=N;i++)
			if(N%i==0){
				factors.add((long) i);
				factors.add(N/i);
			}
		if(N!=1)
			factors.add(N);
		long sum = 0;
		for(long x:factors)
		{
			long M = x-1;
			if(N/M == N%M)
				sum+=M;
		}
		System.out.println(sum);
	}
	
}