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.*;

public class Watermelon {
	public static void main(String[] args) {
	       Scanner sc=new Scanner(System.in);
	       int n=sc.nextInt();
	       int[] arr=new int[n];
	       for(int i=0;i<n;i++)
	    	   arr[i]=sc.nextInt();
	       int count=arr[0]+1;
	      for(int i=0;i<n;i++){
	    	  
	    	  if(i+1<arr.length)
	    	  {
	    		  if(arr[i]==arr[i+1])
	    		  count+=2;
	    	  if(arr[i]<arr[i+1])
	    		  count+=(1+1+arr[i+1]-arr[i]);
	    	  if(arr[i]>arr[i+1])
	    		  count+=(arr[i]-arr[i+1]+2);
	    	  }
	    	  
	      }
	      System.out.println(count);
	}
	 static void display(int[][] arr){
			for(int i=0;i<arr.length;i++){
				for(int j=0;j<arr[i].length;j++){
				//	System.out.println(i);
				System.out.println(arr[i][j]+"         ");
				}
				System.out.println();
			}	
			System.out.println();
		  }

	 static void display(char[] arr){
			for(int i=0;i<arr.length;i++){
				System.out.print(arr[i]+" ");
			}	
			System.out.println();
		
	 }
	 static void display(int[] arr){
			for(int i=0;i<arr.length;i++){
				System.out.print(arr[i]+" ");
			}	
			System.out.println();
		  }
	 static void display(double[] arr){
		// System.out.println();
			for(int i=0;i<arr.length;i++){
				System.out.print(arr[i]+" ");
			}	
			System.out.println();
		
		  }
	 static String str(char[] carr){
		 String str="";
		 for(int i=0;i<carr.length;i++){
			    str=str+carr[i];
			}
		 return str;
	 }
	 
	}

