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:
// D - Sum of Divisors
#include <bits/stdc++.h>
using namespace std;
using ll = long long;

int main(){
	int N; cin>>N;
	ll s = 0;
	for(int m=1; m<=N; ++m){
		int k = N / m;
		s += (ll)k * (k+1) * m / 2;
	}
	cout<< s <<endl;
}