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
/*
 * To change this template, choose Tools | Templates
 * and open the template in the editor.
 */
//package codeforces160;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

/**
 *
 * @author xeyyam
 */
public class B {

    public void run(){
        InputReader reader = new InputReader(System.in);
        int n = reader.nextInt();
        int ans=0;
        int nums[] = new int[n+1];
        
        nums[1] = reader.nextInt();
        ans =  nums[1] + 1;
        
        for(int i = 2 ; i<=n ; i++){
            nums[i] = reader.nextInt();
            
            if( nums[i] >= nums[i-1] ){
                ans += 1 + 1 + nums[i] - nums[i-1];
            }else{
                ans += 1 + 1 + nums[i-1] - nums[i];
            }
            
        } 
       
       System.out.println(ans);
                
    }
    
    public static void main(String args[]){
        new B().run();
    }
    
    
    class InputReader {

        private BufferedReader reader;
        private StringTokenizer tokenizer;
        
        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
            tokenizer = null;
        }
        
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
        
        public int nextInt() {
            return Integer.parseInt(next());
        }
        
        public long nextLong() {
            return Long.parseLong(next());
        }
    }
}