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>
#include <string>
using namespace std;

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