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.Scanner;
 
public class Main {
	public void solve() {
		Scanner in = new Scanner(System.in);
		long N = in.nextLong();
		in.close();
		
		/*
		long testSum = 0;
		for (long i=1; i<=N; i++) {
			if (N / i == N % i) {
				testSum += i;
				System.out.println("m = " + i + " : N mod m = " + (N%i));
			}
		}
		System.out.println("testSum = " + testSum);
		*/
		
		long sum = 0;
		// x is N mod m
		for (long x=1; x<Math.ceil(Math.sqrt(N)); x++) {
			if ((N-x) % x == 0) {
				long m = ((N-x) / x);
				if (N/m == N%m) {
					sum += m;
					//System.out.println("m = " + m + " : N mod m = " + (N%m));
				} else {
					//System.out.println("pass : m = " + m + " : N mod m = " + (N%m));
				}
			}
		}
		System.out.println(sum);
	
	}
	
	public static void main(String[] args) {
		Main main = new Main();
		main.solve();
	}
 
}