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 <iostream>
#define ll long long

using namespace std;

int main()
{
  int N; cin>>N;
  ll ans=0;
  for(int i=1; i<=N; i++){
    for(int j=i; j<=N; j+=i){
      ans+=j;
    }
  }
  cout<<ans<<endl;
  return 0;
}