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 d2_162_B {

    /**
     * @param args
     */
    public static void main(String[] args) {
        // TODO Auto-generated method stub
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
//      int a[]=new int[n];
//      int b[]=new int[n];
//      for(int i=0;i<n;i++)
//          a[i]=sc.nextInt();
//      int cost=a[0]+1;
//      for(int i=0 ;i<n-1;i++)
//      {
//          if(a[i]>a[i+1])
//          {
//              b[i]=a[i]-a[i+1];
//          }
//          else if(a[i]<a[i+1])
//          {
//              b[i]=a[i];
//              b[i+1]=a[i+1]-a[i];
//          }
//          else
//              b[i]=a[i];
//      }
//      if(a[0]>a[1])
//      {
//          for(int i=0;i<n;i++)
//          {
//              cost+=b[i]+2;
//          }
//      }
//      else
//      {
//          cost+=1;
//          for(int i=1;i<n;i++)
//          {
//              cost+=b[i]+2;
//          }
//      }
//      System.out.println(cost);
        int curht=0,treeht,steps=0;
        for(int i=0;i<n;i++)
        {
            treeht=sc.nextInt();
            if(curht<treeht)
            {
                steps+=treeht-curht+1;
                steps++;
            }
            else
            {
                steps+=curht-treeht+1;
                steps++;
            }
            curht=treeht;
        }
        System.out.println(steps-1);
        

    }

}
