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.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;

 



public class BUFFER2 {
		public static void main(String[] args) throws NumberFormatException, IOException {
		InputStreamReader ir=new InputStreamReader(System.in);
		BufferedReader br=new BufferedReader(ir);
		int n=Integer.parseInt(br.readLine());
		//String[] s=br.readLine().trim().split(" ");
		//long n=Long.parseLong(br.readLine());
		//String[] s2=br.readLine().trim().split(" ");
		int j=2*n-1;
		//ArrayList<Integer>al=new ArrayList();
		int mm1=Integer.parseInt(br.readLine());
		//al.add(mm);
		j=j+mm1;
		for(int i=1;i<n;i++)
		{	int mm2=Integer.parseInt(br.readLine());
			//al.add(mm2);
			j=j+Math.abs(mm1-mm2);
			mm1=mm2;
		}
		System.out.println(j);
		}
		
		
		
		}
	


