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 <bits/stdc++.h>
using namespace std;
int n,m;
long long k;
long long ans;
int main()
{
    cin>>n;
    for(int i=1;i<=n;++i)
    {
        long long pom=n/i;
        ans+=pom*(pom+1)/2*i;
    }
    cout<<ans;
}