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;

#define int long long int

signed main()
{
    int n,i,j;
    cin>>n;
    int sum=(n*(n+1))/2;
    for(i=2;i<=n;i++)
    {
        for(j=i;j<=n;j+=i) sum+=(j);
    }
    cout<<sum;
}