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 MOD 1000000007
using ll=long long;


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