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 <stdio.h>
#define LL long long
LL ans;
int main(){
	int n,i,m,a,b;
	scanf("%d",&n);
	for(i=1;i<=n;i++){
		m=n/i;
		a=i,b=a+(m-1)*i;
		ans+=(LL)(a+b)*m/2;
	}
	printf("%lld\n",ans);
	return 0;
}