Squirrel Liss loves nuts. There are n trees (numbered 1 to n from west to east) along a street and there is a delicious nut on the top of each tree. The height of the tree i is hi. Liss wants to eat all nuts.

Now Liss is on the root of the tree with the number 1. In one second Liss can perform one of the following actions:

  * Walk up or down one unit on a tree. 
  * Eat a nut on the top of the current tree. 
  * Jump to the next tree. In this action the height of Liss doesn't change. More formally, when Liss is at height h of the tree i (1 ≤ i ≤ n - 1), she jumps to height h of the tree i + 1. This action can't be performed if h > hi + 1. 



Compute the minimal time (in seconds) required to eat all nuts.

Input

The first line contains an integer n (1 ≤ n ≤ 105) — the number of trees.

Next n lines contains the height of trees: i-th line contains an integer hi (1 ≤ hi ≤ 104) — the height of the tree with the number i.

Output

Print a single integer — the minimal time required to eat all nuts in seconds.

Examples

Input

2
1
2


Output

5


Input

5
2
1
2
1
1


Output

14
import java.io.IOException;
//You can include standard Java language libraries that you want use.//

import java.util.*;

public class Task{

/*      public static StreamTokenizer in;
        public static PrintStream out;

        public static String readString() throws IOException {
            in.nextToken();
            return  in.sval;
            }

        public static double readDouble() throws IOException {
            in.nextToken();
            return in.nval;
            }

        public static int readInt() throws IOException {
            in.nextToken();
            return (int) in.nval;
        }*/

    
    int nod(int a, int b){
        int ada=Math.max(a,b);
        int adb=Math.min(a,b);
        
        while (ada%adb!=0){
            int curada=ada;
            ada=adb;
            adb=curada%adb;
        }
        return adb;
    }
    
     public void solution(String inputFilePath, String usrOutputFilePath ) throws IOException{       
//       in = new StreamTokenizer(new FileReader(inputFilePath) );

         Scanner rd = new Scanner(System.in);

         
            int n=rd.nextInt();
            
            int sum=0;int curh=0;
            for (int i = 0; i < n; i++) {
                int h=rd.nextInt();
                sum+=Math.abs(h-curh)+2;
                curh=h;
            }
            
            System.out.println(sum-1);
            
            rd.close();
             return;
             
    }

    public static void main(String[] args) throws IOException {
        Task test = new Task();
        test.solution("in.txt", "out.txt");

    }
     
}