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>
#define ll long long
using namespace std;

int main(){
    ll int n,k,sum=0;
    cin >> n;
    for (int i=1; i<=n; i++){
        k=n/i;
        sum+=k*(k+1)/2*i;
    }
    cout << sum;
}