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
/**
 * Created by Omar on 1/7/2016.
 */

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

public class Roadside {
    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n=Integer.parseInt(br.readLine());
        //String[] parts=br.readLine().split(" ");
        int[]a= new int[n];
        for(int i=0;i<n;i++){a[i]=Integer.parseInt(br.readLine());}

        int answer=a[0];
        for(int i=0;i<n-1;i++) {

        answer+=Math.abs(a[i]-a[i+1]);
        }
        System.out.println(answer+2*n-1);
        br.close();
    }
}
