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.HashSet;
import java.util.Scanner;
import java.util.Set;
import java.util.ArrayList;
import java.util.Collections;
import java.text.DecimalFormat;
import java.lang.Math; 
public class Lo {
    public static void main(String[] args){
      Scanner sc = new Scanner(System.in);
      int n = sc.nextInt();
      ArrayList<Integer> A = new ArrayList<Integer>();
      for(int i = 0; i < n; i++){
          A.add(sc.nextInt());
      }
      int count = 0;
      for(int i = 0; i < n-1; i++){
          if(A.get(i)>A.get(i+1) && i==0){
              count += 2*A.get(i)-A.get(i+1)+1;
          }
          else if(A.get(i)<=A.get(i+1) && i==0){
              count += A.get(i+1)+1;
          }
          else if(A.get(i)<=A.get(i+1)){
              count += A.get(i+1)-A.get(i)+1;
          }
          else if(A.get(i)>A.get(i+1)){
              count += A.get(i)-A.get(i+1)+1;
          }
      }
      count += n;
      if(A.size()==1){
          count = A.get(0)+1;
      }
      System.out.println(count);
    }
}