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>

typedef long long ll;

int main() {
  ll N; std::cin >> N;
  ll ans = 0;
  for (ll x = 1; x <= N; ++x) {
    ll y = N/x;
    ans += y * (y+1) * x / 2;
  }
  std::cout << ans << "\n";

  return 0;
}