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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.sql.Time;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Date;
import java.util.StringTokenizer;
import java.util.Vector;

public class home {
	public static void main(String[] args) {
		
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskA solver = new TaskA();
		solver.solve(1, in, out);
		out.close();
	}

	// ---------------------------------------------------
	static class TaskA {

		public void solve(int testNumber, InputReader in, PrintWriter out) {
			// -------- Write Task Code ----------
			
		     int n = in.nextInt();
		     int[] steps = new int [n];
		     for(int i =0 ; i< n; i++){
		    	 steps[i] = in.nextInt();
		     }
		     int NumSteps = 0;
		     
			 for(int j=0 ; j< n ; j++){
				 if(j>0) NumSteps ++ ;
				 if(j==0){
					 NumSteps += steps[j];
					 NumSteps ++ ;
				 }else{
					 NumSteps +=  Math.abs(steps[j]-steps[j-1]);
					 NumSteps ++ ;
				 }
			 }
			 out.println(NumSteps);
			
			// ------- finish Task Code ---------
		}
	}

	

	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 32768);
			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 Long nextLong() {
			return Long.parseLong(next());
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

	}
}
