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 rep(i,n) for(int i=0;i<n;i++) 
using namespace std;

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