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: Time Limit Exceeded)

import java.io.*;

public class Main{
  public static void main(String... args) throws IOException {
    BufferedReader stdin = new BufferedReader(new InputStreamReader(System.in));
    String line = stdin.readLine();
    long n = Long.parseLong(line);
    System.err.println(n);

    if (n == 3) {
      System.out.println(2);
      return;
    }
    
    long sum = 0;
    for (int i=(int)Math.sqrt(n); i < n; i++) {
      long div = n / i;
      long mod = n % i;
      if (div == mod) {
        sum += i;
      }
    }

    System.out.println(sum);
  }
}