The Fair Nut lives in n story house. a_i people live on the i-th floor of the house. Every person uses elevator twice a day: to get from the floor where he/she lives to the ground (first) floor and to get from the first floor to the floor where he/she lives, when he/she comes back home in the evening. 

It was decided that elevator, when it is not used, will stay on the x-th floor, but x hasn't been chosen yet. When a person needs to get from floor a to floor b, elevator follows the simple algorithm: 

  * Moves from the x-th floor (initially it stays on the x-th floor) to the a-th and takes the passenger. 
  * Moves from the a-th floor to the b-th floor and lets out the passenger (if a equals b, elevator just opens and closes the doors, but still comes to the floor from the x-th floor). 
  * Moves from the b-th floor back to the x-th. 

The elevator never transposes more than one person and always goes back to the floor x before transposing a next passenger. The elevator spends one unit of electricity to move between neighboring floors. So moving from the a-th floor to the b-th floor requires |a - b| units of electricity.

Your task is to help Nut to find the minimum number of electricity units, that it would be enough for one day, by choosing an optimal the x-th floor. Don't forget than elevator initially stays on the x-th floor. 

Input

The first line contains one integer n (1 ≤ n ≤ 100) — the number of floors.

The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 100) — the number of people on each floor.

Output

In a single line, print the answer to the problem — the minimum number of electricity units.

Examples

Input

3
0 2 1


Output

16

Input

2
1 1


Output

4

Note

In the first example, the answer can be achieved by choosing the second floor as the x-th floor. Each person from the second floor (there are two of them) would spend 4 units of electricity per day (2 to get down and 2 to get up), and one person from the third would spend 8 units of electricity per day (4 to get down and 4 to get up). 4 ⋅ 2 + 8 ⋅ 1 = 16.

In the second example, the answer can be achieved by choosing the first floor as the x-th floor.
import com.sun.org.apache.xalan.internal.xslt.Process;

import java.io.*;
import java.util.*;

public class main {
    public static void main(String[] args) throws IOException {
        init();//"prizes.in", "prizes.out");
        int n = nextInt();
        int y[] = new int[n + 1];
        for (int i = 1; i < y.length; i++) {
            y[i] = nextInt();
        }
        int minE = Integer.MAX_VALUE;
        for (int i = 1; i <= n; i++) {
            int countE = 0;
            for (int j = 1; j <= n; j++) {
                int sum = Math.abs(i - j) + (j - 1) + Math.abs(i - 1);
                sum += Math.abs(i - 1) + (j - 1) + Math.abs(j - i);
                countE += y[j] * sum;
            }
            minE = Math.min(minE, countE);
        }
        pw.println(minE);
        pw.close();
    }

    static StringTokenizer st;
    static BufferedReader sc;
    static PrintWriter pw;

    static String next() throws IOException {
        while (st == null || !st.hasMoreElements()) {
            st = new StringTokenizer(sc.readLine());
        }
        return st.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    static void init(String in, String out) throws IOException {
        sc = new BufferedReader(new FileReader(in));
        pw = new PrintWriter(out);
    }

    static void init() {
        sc = new BufferedReader(new InputStreamReader(System.in));
        pw = new PrintWriter(System.out);
    }
}

class DSU {
    int parent[];
    public DSU(int n){
        parent = new int[n];
        for (int i = 0; i < n; i++) {
            parent[i] = i;
        }
    }

    int get(int i){
        if (i == parent[i]){
            return i;
        }
        int p = get(parent[i]);
        parent[i] = p;
        return p;
    }

    boolean union(int a, int b){
        a = get(a);
        b = get(b);
        if (a == b) return false;
        parent[a] = b;
        return true;
    }
}