You are given a positive integer n greater or equal to 2. For every pair of integers a and b (2 ≤ |a|, |b| ≤ n), you can transform a into b if and only if there exists an integer x such that 1 < |x| and (a ⋅ x = b or b ⋅ x = a), where |x| denotes the absolute value of x.

After such a transformation, your score increases by |x| points and you are not allowed to transform a into b nor b into a anymore.

Initially, you have a score of 0. You can start at any integer and transform it as many times as you like. What is the maximum score you can achieve?

Input

A single line contains a single integer n (2 ≤ n ≤ 100 000) — the given integer described above.

Output

Print an only integer — the maximum score that can be achieved with the transformations. If it is not possible to perform even a single transformation for all possible starting integers, print 0.

Examples

Input

4


Output

8

Input

6


Output

28

Input

2


Output

0

Note

In the first example, the transformations are 2 → 4 → (-2) → (-4) → 2.

In the third example, it is impossible to perform even a single transformation.
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

/**
 * @author Don Li
 */
public class FunWithIntegers {
    
    int[] parent;
    
    void solve() {
        int n = in.nextInt();
        
        parent = new int[n + 1];
        Arrays.fill(parent, -1);
        
        for (int i = 2; i <= n; i++) {
            for (int j = i + i; j <= n; j += i) {
                union(i, j);
            }
        }
        
        int[] sz = new int[n + 1];
        for (int i = 2; i <= n; i++) {
            int j = find(i);
            sz[j]++;
        }
        int[][] comp = new int[n + 1][];
        for (int i = 2; i <= n; i++) {
            comp[i] = new int[sz[i]];
        }
        for (int i = 2; i <= n; i++) {
            int j = find(i);
            comp[j][--sz[j]] = i;
        }
        
        long ans = 0;
        for (int i = 2; i <= n; i++) {
            long tot = 0;
            for (int x : comp[i]) {
                for (int y = x + x; y <= n; y += x) tot += y / x;
            }
            ans = Math.max(ans, tot);
        }
        out.println(ans * 4);
    }
    
    int find(int i) {
        if (parent[i] < 0) return i;
        return parent[i] = find(parent[i]);
    }
    
    void union(int i, int j) {
        int u = find(i), v = find(j);
        if (u == v) return;
        if (parent[u] > parent[v]) {
            int tmp = u; u = v; v = tmp;
        }
        parent[u] += parent[v];
        parent[v] = u;
    }
    
    public static void main(String[] args) {
        in = new FastScanner(new BufferedReader(new InputStreamReader(System.in)));
        out = new PrintWriter(System.out);
        new FunWithIntegers().solve();
        out.close();
    }
    
    static FastScanner in;
    static PrintWriter out;
    
    static class FastScanner {
        BufferedReader in;
        StringTokenizer st;
        
        public FastScanner(BufferedReader in) {
            this.in = in;
        }
        
        public String nextToken() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(in.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        
        public int nextInt() {
            return Integer.parseInt(nextToken());
        }
        
        public long nextLong() {
            return Long.parseLong(nextToken());
        }
        
        public double nextDouble() {
            return Double.parseDouble(nextToken());
        }
    }
}
