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;

int main(){
	int N; cin>>N;
	long long  s = 0;
	for(int d=1; d<=N; ++d)
		for(int k=d; k<=N; k+=d) s += k;
	cout<< s <<endl;
}