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 rep(i,n) for(ll i=1; i<=(ll)(n); i++)
using ll = long long int;

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