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

using namespace std;

int main() {
  int n;
  scanf("%d", &n);
  ll o = 0;
  for(ll i = 1; i <= n; i++) o += i * (n / i + 1) * (n / i) / 2;
  printf("%lld\n", o);
}