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;

int main(){
  int64_t n;
  cin >>n;
  int64_t ans=0;
  for(int64_t i=1;i<=n;i++){
    for(int64_t j=i;j<=n;j+=i){
      ans+=j;
    }
  }
  cout <<ans<<endl;
  return 0;
}