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.*;

public class Main {

    public static void main(String args[]) {

        // 入力
        Scanner sc = new Scanner(System.in);
        long n = Long.parseLong(sc.next());
        sc.close();

        // 主処理
        long[] divCount = new long[10000001];
        Arrays.fill(divCount, 1);
        for (int i = 2; i < 10000001; i++) {
            for (int j = i; j < 10000001; j += i) {
                divCount[j]++;
            }
        }
        long result = 0;
        for (int i = 1; i <= n; i++) {
            result += (long) i * divCount[i];

        }

        // 出力
        System.out.println(result);
    }
}