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 ll = long long;
using namespace std;

int main() {
    int n;cin>>n;
    ll ans=0;
    for (int i=1;i<=n;i++) {
        ll d=n/i;
        ans+=d*(d+1)/2*i;
    }
    cout<<ans<<endl;
    return 0;
}