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;

long long s(long n){
  return n * (n+1) / 2;
}

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