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.Scanner;

/**
 *
 * @author ACM
 */
public class RoadsideTreesSimplifiedEdition {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);int z =0;
        int n = in.nextInt();
        int ar[]  = new int[n];
        int coutnSecound=0;
        int height=0;
        for (int i = 0,j; i < ar.length; i++) {
            j = in.nextInt();
                if(j>height&&i==0){
                   coutnSecound+=j+2;height=j;}
                else if(j>=height&&i!=0){
                    coutnSecound+=(j-height+2);
                    height=j;
                }
                else if(height>=j&&i!=0){
                    coutnSecound+=(height-j)+2;
                    height=j;}
                  
                    
                    
            
           
            
      
} System.out.println(--coutnSecound);
        
    }

}
