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.StringTokenizer;

public class B {
    public static void main(String[] args) throws IOException{
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer sb=new StringTokenizer(br.readLine());
        int n= Integer.parseInt(sb.nextToken());
        int[] h=new int[n];
        for(int i=0;i<n;i++) {
            sb=new StringTokenizer(br.readLine());
            h[i]=Integer.parseInt(sb.nextToken());
        }
        int result=0;
        int currentHeight=0;
        for(int i=0;i<n-1;i++) {
            if(h[i]<=h[i+1]) {
                result+=(h[i]-currentHeight);
                result+=1;
                result+=1;
                currentHeight=h[i];
            } else {
                result+=(h[i]-currentHeight);
                result+=1;
                result+=(h[i]-h[i+1]);
                result+=1;
                currentHeight=h[i+1];
            }
        }
        result+=(h[n-1]-currentHeight+1);
        System.out.println(result);
    }
}
