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>
using namespace std;
long long int n,f[10000005],cnt,ans,s;
int main(){
	int i,j,k;
	cin>>n;
	for(i=1;i<=n;i++){
		for(j=i;j<=n;j+=i){
			f[j]++;
		}
	}
	for(i=1;i<=n;i++)ans+=i*f[i];
	cout<<ans;
}