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
/* package whatever; // don't place package name! */

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

/* Name of the class has to be "Main" only if the class is public. */
public final class Ideone
{
    public static void main (String[] args) throws java.lang.Exception
    {
        Scanner in = new Scanner(System.in);
        int num=in.nextInt();
        int[] arr= new int[num];
        for(int i=0;i<num;i++){
            arr[i]=in.nextInt();
        }
        int ans=arr[0]+1;
        
        
        int j=1;
        //for(int j=1;j<=num-1;j++){// 
        if(num>1){
            int diff=arr[1]-arr[0];
        do{
            if(diff>=0)
              ans=ans+diff+2;
            else
              ans=ans+Math.abs(diff)+2;
        //System.out.println(ans);    
        if(j<num-1)   
        diff=arr[j+1]-arr[j];     
              
        j++;      
              
        }while(j!=num);}
        System.out.println(ans);
    }
}