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 MyClass {
    public static void main(String args[]) {
      Scanner sc = new Scanner(System.in);
      int n = sc.nextInt();
      int i,h=0;
      int a[] = new int[n];
      for(i=0 ;i< n;i++){
          a[i]=sc.nextInt();
      }
      int count =0;
      for(i=0;i<n;i++){
          count += a[i]-h;
          ++count;
          if((i+1)<n&&a[i+1]<a[i]){
              count +=a[i]-a[i+1];
            h=a[i+1];      
          }
          else
            h=a[i];
          ++count;
      }
      System.out.println(count-1);
    }
}