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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.IO;
using static System.Math;
namespace AtCoder
{
    class Program
    {
        static public long[] Sarray() { return ReadLine().Split().Select(long.Parse).ToArray(); }
        static public List<long> Slist() { return ReadLine().Split().Select(long.Parse).ToList(); }
        static long Mod = (long)1e9 + 7;
        static void Main(string[] args)
        {
            //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
            var N = Sarray()[0];
            // k
            var div = divisors(N);
            var ans = 0L;
            // m=N/k-1
            foreach (var d in div)
            {
                var m = N / d - 1;
                if (m != 0 && N / m == N % m)
                    ans += m;
            }
            WriteLine(ans);
            //Out.Flush();
        }
        static HashSet<long> divisors(long n)
        {
            var div = new HashSet<long>();
            for (long i = 1; i * i <= n; ++i)
            {
                if (n % i == 0)
                {
                    div.Add(i);
                    if (i != n / i)
                        div.Add(n / i);
                }
            }
            return div;
        }
    }
}