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.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Scanner;

public class Task265B {

	public static void main(String... args) throws NumberFormatException,
			IOException {
		Solution.main(System.in, System.out);
	}

	static class Solution {

		public static void main(InputStream is, OutputStream os)
				throws NumberFormatException, IOException {
			PrintWriter pw = new PrintWriter(os);
			Scanner s = new Scanner(is);

			int n = s.nextInt();

			int retVal = 0;

			int h = s.nextInt();
			retVal += h+1;

			for (int i = 1; i < n; i++) {
				int curH = s.nextInt();
				retVal += Math.abs(curH - h) + 2;
				h = curH;
			}
			pw.write(retVal+"");
			
			pw.flush();
			s.close();
		}
	}

}
