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 java.util.*;
import java.lang.*;

public class HelloWorld{
    public static int calculateOneFloor(int eFloor, int homeFloor) {
        int first = Math.abs(homeFloor - eFloor);
        int second = Math.abs(homeFloor - 1);
        int third = Math.abs(eFloor - 1);
        
        return (2 * (first + second + third));
    }
    
    public static int calculateTotalCost(int eFloor, List<Integer> residents) {
        int sum = 0;
        for (int i = 1; i < residents.size(); i++) {
            sum += (residents.get(i) * calculateOneFloor(eFloor, i));
        }
        return sum;
    }
    
    public static int findMin(List<Integer> residents) {
        int minSum = Integer.MAX_VALUE;
        boolean allZeros = true;
        
        for (int i = residents.size() - 1; i > 0; i--) {
            if (residents.get(i) != 0) {
                allZeros = false;
            }
            if (!allZeros) {
                int sum = calculateTotalCost(i, residents);
                if (sum < minSum) {
                    minSum = sum;
                }
            }
        }
        
        if (allZeros) {
            return 0;
        }
        
        return minSum;
    }
    
    public static void main(String []args){
    Scanner scanner = new Scanner(System.in);
    List<Integer> list = new ArrayList<Integer>();
    while (scanner.hasNextInt()) {
      list.add(scanner.nextInt());
    }
    scanner.close();
    System.out.println(findMin(list));
    }
}