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: Runtime Error)


import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Scanner;

public class Main {
	public static void main(final String[] args) {
		@SuppressWarnings("resource")
		final Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
		final long N = in.nextInt();
		System.out.println(solve(N));
	}

	public static long solve(long N) {
		long ans = 0;
		for (long x = 1; ; ++x) {
			if (N % x != 0)
				continue;
			final long m = N / x - 1;
			if (m <= x)
				break;
			ans += m;
		}
		return ans;
	}
}