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>

int main() {
	int N; scanf("%d", &N);
	long long ans = 0;
	for (int i = 1; i <= N; i++) {
		long long num = N / i;
		ans += i * (num * (num + 1) / 2);
	}
	printf("%lld", ans);
	return 0;
}