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.*;
public class B {
    public static void main (String[]ar)throws Exception{
        BufferedReader read = new BufferedReader (new InputStreamReader(System.in));
        
        int trees = Integer.parseInt(read.readLine());
        
        int[] t = new int[trees];
        for(int i=0;i<trees;i++)
            t[i] = Integer.parseInt(read.readLine());
            
        int sec = 0,pos = 0;
        boolean jump = false;
        
        for(int i=0;i<trees;i++){
           
            if(!jump){
                sec += t[i];
            }else{
                sec += t[i] - pos + 1;
            }
            
            if(i < trees - 1 && t[i+1] < t[i]){
                sec += t[i] - t[i+1];
                jump = true;
                pos = t[i+1];
            }else{
                pos = t[i];
                jump = true;
            }
            
                
            sec++;
        }
        System.out.println(sec);
    }
}