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 ll long long int
using namespace std;
int main()
{
  ll n,sum=0;
  cin>>n;
  for(ll i =1;i<=n;i++)
  {
    sum=sum+(i*(n/i)*(n/i+1))/2;
  }
  cout<<sum<<endl;
}