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.*;

/**
 *
 * @author DHA
 */
public class JavaApplication1 {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) throws IOException {
        // TODO code application logic here
        int n,h = 0;
        
         BufferedReader r = new BufferedReader (new InputStreamReader (System.in));
         n=Integer.parseInt(r.readLine());
         int[] he=new int[n];
         for(int i=0;i< n;i++)
             he[i]=Integer.parseInt(r.readLine());
         int t = 0;
          for(int i=0;i< n;i++)
          {
              if(he[i]>=h && i!=0)
              { 
                t=t+he[i]-h;
                t=t+1;
              }
              
             else
              {
              if(i!=0)
              {t=t+he[i-1]-he[i];
              t=t+1;
              }
              else
                  t=he[i];
             }
              t=t+1;
              h=he[i];
             
              
          }
            System.out.println(t);  
         
//         s= r.readLine().toCharArray();
//         t= r.readLine().toCharArray();
//         int si=0;
//        
//         for(int i=0;i<t.length;i++)
//         {
//             if(si==s.length)
//                 break;
//             if(t[i]==s[si])
//                 si++;
//         }
//         
//         if(si==s.length)
//         System.out.println(si);
//         else
//          System.out.println(si+1);    
    }
}
