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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.util.Arrays;

public class A1084{
    public static void  main(String[] args) throws IOException{
        Reader.init(System.in);
        int n=Reader.nextInt();
        int []a=new int [n];
        int x=0; int mid=0;
        int units=0;
        int units2=0; int units3=0;
        for(int i=0;i<n;i++){

            a[i]=Reader.nextInt();
        }
        if (a.length%2==0){
            mid=a.length/2;
            x=mid-1; }
        else{
            mid=(a.length+1)/2;
            x=mid-1;  }
        for(int s=0;s<a.length;s++){
            if (s<x){
                int sum1=x-s;
                int sum2=s-0;
                int half=2*(sum1+sum2);
                int total=2*half;
                units=total*a[s];
                // System.out.println(units);
                }
            else if(s>x){
                int sum1=s-x;
                int sum2=s;
                int sum3=x;
                int totaltime=2*(sum1+sum2+sum3);
                units2=totaltime*a[s];
            }
            else{
                int sum1=x-s;
                int sum2=s-0;
                int half=2*(sum1+sum2);
                int total=2*half;
                units3=total*a[s];
              //  System.out.println(units3);
            }
 
        }
      
        int finalans=units+units2+units3;
            System.out.println(finalans);
           

        

    }

}
class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    /** call this method to initialize reader for InputStream */
    static void init(InputStream input) {
        reader = new BufferedReader(
                     new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");
    }

    /** get next word */
    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                   reader.readLine() );
        }
        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt( next() );
    }
    
    static double nextDouble() throws IOException {
        return Double.parseDouble( next() );
    }
}