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