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

 public class cf64
 {
   public static void main(String args[]) throws Exception {
     
     try{
       BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
     
       String s[]=br.readLine().split(" ");
       int  n=Integer.parseInt(s[0]);
       int h[]=new int[n];
       for(int i=0;i<n;i++){
         String s1=br.readLine();
         h[i]=Integer.parseInt(s1);
         }
         int t=n+n-1,hi=0;
         for(int i=0;i<n;i++){
           t+=Math.abs(h[i]-hi);
           hi=h[i];
         }
         System.out.println(t);
         }catch(Exception e){
           return;
         }
         }
         }