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 <cstdio>
#define ll long long
int main(){
	ll n, s = 0;
	scanf("%lld", &n);
	for (int i = 1; i <= n; i++) s += (i + n / i * i) * (n / i) / 2;
	printf("%lld\n", s);
}