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.util.Arrays;
import java.util.StringTokenizer;

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

    static class Task {

	public void solve(InputReader in, PrintWriter out) {
	    int n = in.nextInt();
	    int[] h = new int[n];
	    for (int i = 0; i < n; i++) {
		h[i] = in.nextInt();
	    }
	    int s = h[0] + 1;
	    for (int i = 1; i < n; i++) {
		s += 1 + Math.abs(h[i] - h[i - 1]) + 1;
	    }
	    out.println(s);
	}

    }

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

    }
}