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()
{
  int n;
  cin>>n;
  map<int,int>m;
  long long ans=0;
  for(int i=1;i<=n;i++)
  {
    long long t=n/i;
    ans+=(t*(t+1)/2)*i;
  }
 
  cout<<ans<<endl;
  
  return 0;
}