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.
 */

/**
 *
 * @author Hoang
 */
import java.io.*;
import java.util.*;

public class Main {

    private static BufferedReader reader;
    private static PrintWriter out;
    private static StringTokenizer tokenizer;
    //private final static String filename = "filename";

    private static void init(InputStream input, OutputStream output) throws IOException {
        reader = new BufferedReader(new InputStreamReader(input));
        out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(output)));
        //reader = new BufferedReader(new FileReader(filename + ".in"));
        //out = new BufferedWriter(new FileWriter(filename + ".out"));
        tokenizer = new StringTokenizer("");
    }

    private static String nextLine() throws IOException {
        return reader.readLine();
    }

    private static String next() throws IOException {
        while (!tokenizer.hasMoreTokens())
            tokenizer = new StringTokenizer(nextLine());
        return tokenizer.nextToken();
    }

    private static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    private static long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    private static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) throws IOException {
        init(System.in, System.out);
        int n = nextInt();
        int prev = nextInt();
        int time = prev + 1;
        //long startTime = System.currentTimeMillis();
        for (int i = 1; i < n; i++) {
            int current = nextInt();
            if (current >= prev)
                time += current - prev + 2;
            else
                time += prev - current + 2;
            prev = current;
        }
        out.println(time);
        //long runTime = System.currentTimeMillis() - startTime;
        //out.write(runTime + "\n");
        out.close();
        System.exit(0);
    }
}