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;
long long n,i,j,nr;
int main()
{

    cin>>n;
    for(j=1;j<=n;j++)
        for(i=j;i<=n;i+=j)
        if(i%j==0)
        nr+=i;
    cout<<nr;

}