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.util.*;
import java.lang.*;
import java.io.*;
public class RoadSide_Trees {

	public static void main(String[] args) throws java.lang.Exception
    {		
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int t=Integer.parseInt(br.readLine()),h[]=new int[t];
		for(int i=0;i<t; i++) {
			h[i]=Integer.parseInt(br.readLine());
		}
		int sum=t+t-1+h[0];
		for(int i=0; i<t-1; i++) {
			sum+=Math.abs(h[i+1]-h[i]);
		}
		System.out.println(sum);
	}

}
