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>
#define ll long long
using namespace std;
int main(){
	ios_base::sync_with_stdio(false); cin.tie(NULL);
	ll n, ans = 0; cin>>n;
	for(ll i = 1;i<=n;i++){
		ans += i*(n / i)*(n/i + 1) / 2;
	}
	cout<<ans;
}