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.StringTokenizer;

/**
 * @author artyom
 */
public class RoadsideTreesSimplifiedEdition implements Runnable {
    private BufferedReader in;
    private PrintStream out;
    private StringTokenizer tok;

    private void solve() throws IOException {
        int time = 0, pos = 0;
        for (int i = 0, n = nextInt(); i < n; i++) {
            int h = nextInt();
            if (i > 0) {
                time++; // Jump
            }
            if (h < pos) {
                time += pos - h; // Get down to be able to jump
            } else {
                time += h - pos; // Get to the top
            }
            time++; // Eat the nut
            pos = h;
        }
        out.println(time);
    }

    //--------------------------------------------------------------
    public static void main(String[] args) {
        new RoadsideTreesSimplifiedEdition().run();
    }

    @Override
    public void run() {
        try {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = System.out;
            tok = null;
            solve();
            in.close();
        } catch (IOException e) {
            System.exit(0);
        }
    }

    private String nextToken() throws IOException {
        while (tok == null || !tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine());
        }
        return tok.nextToken();
    }

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