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.*;
import java.util.*;

public class cakeminator {
	
	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub
		Reader.init(System.in);
		int n=Reader.nextInt();
		int arr[]=new int[n];
		for(int i=0;i<n;i++)
			arr[i]=Reader.nextInt();
		int h=arr[0];
		int time=arr[0]+1;
		for(int i=1;i<n;i++) {
			time+=2;
			if(h>arr[i]) {
				time+=h-arr[i];
				h=arr[i];
			}
			else {
				time+=arr[i]-h;
				h=arr[i];
			}
			
		}
		System.out.println(time);
		
		}
		
		
		
	
	}


class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    /** call this method to initialize reader for InputStream */
    static void init(InputStream input) {
        reader = new BufferedReader(
                     new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");
    }

    /** get next word */
    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                   reader.readLine() );
        }
        return tokenizer.nextToken();
    }
    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }
	
    static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }
}

