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 {
    static Scanner scanner = new Scanner(System.in);

    public static void main(String[]$) {
        long n = scanner.nextLong();
        long ans = 0;
        for (long i = 1; i * i <= n; i++) {
            if (n % i == 0) {
                long m1 = i - 1;
                if (i != 1 && n / m1 == n % m1) {
                    ans += m1;
                }
                long m2 = n / i - 1;
                if (i * i != n && n / m2 == n % m2) {
                    ans += m2;
                }
            }
        }
        System.out.println(ans);
    }
}