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.*;

public class trees
{
    public static void main(String[] a) throws IOException
    {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter writer = new PrintWriter(new OutputStreamWriter(System.out));

        int n = Integer.parseInt(reader.readLine().trim());

        int[] h = new int[n];
        int before = h[0] = Integer.parseInt(reader.readLine().trim());
        int sum  = 0;

        for(int i = 1; i < n; i++)
        {
            h[i] = Integer.parseInt(reader.readLine().trim());
            sum += Math.abs(h[i]-before);
            before = h[i];

        }
        writer.println(sum+n+n-1+h[0]);
        writer.flush();
        writer.close();


    }

}
