Problem: For a positive integer X, let f(X) be the number of positive divisors of X.

Given a positive integer N, find \sum_{K=1}^N K\times f(K).

Constraints

* 1 \leq N \leq 10^7

Input

Input is given from Standard Input in the following format:


N


Output

Print the value \sum_{K=1}^N K\times f(K).

Examples

Input

4


Output

23


Input

100


Output

26879


Input

10000000


Output

838627288460105

Solution (in CPP):

Solution:
#include <iostream>
using namespace std;
int main()
{
    long long int n, i, j, s = 0,sum=0;
    cin >> n;
    for (i = 1; i <= n; i++)
    {
        for (j = i; j <= n; j=j+i)
        sum+=j;
    }
    cout << sum;
}