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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;

public class Main {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		long n = Long.parseLong(br.readLine());

		ArrayList<Long> list = divisor(n);
		long sum = 0;
		for (long l : list) {
			long m = n / l - 1;
			if (m == 0)
				continue;

			if (n / m == n % m) {
				sum += m;
			}
		}

		System.out.println(sum);
	}

	public static final ArrayList<Long> divisor(final long n) {
		final ArrayList<Long> list = new ArrayList<>();

		for (long i = 1; i * i <= n; i++) { // √n
			if (n % i == 0) {
				list.add(i); // a x b
				if (i != n / i) {
					list.add(n / i); // b x a (逆向き)
				}
			}
		}
		return list;
	}
}