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 JAVA):

Solution:
import java.util.Scanner;

public class Main {
	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int[] dp = new int[N + 1];
		long res = 0;
		for (int i = 1; i <= N; i++) {
			long pos = i;
			dp[(int) pos] += 1;
			while (pos + i <= N) {
				pos += i;
				dp[(int) pos] += 1;
			}
			if (dp[i] < 0) {
				System.out.println(dp[i]);
			}
			res += i * (long) dp[i];
		}
		System.out.println(res);
	}
}