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.util.*;

public class Main {
	Scanner sc = new Scanner(System.in);

	void doIt() {
		long n = sc.nextLong();
		long sum = 0;
		for(long i = 1; i * i < n; i++) {
			if(n % i == 0) {
				long m = n / i - 1;
				if(n / m == n % m) {
					sum += m;
				}
			}			
		}
		System.out.println(sum);
		
	}
	
	
	public static void main(String[] args) {
		new Main().doIt();
	}
}