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 nazir
 */
public class RoadsideTrees {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);

        int numberOftrees = scanner.nextInt();
        int[] heightOfTrees = new int[numberOftrees];
        int seconds = 0;
        for (int i = 0; i < heightOfTrees.length; i++) {
            heightOfTrees[i] = scanner.nextInt();
            if (i == 0) {
                seconds += heightOfTrees[i] + 1;
            } else if (heightOfTrees[i] >= heightOfTrees[i - 1]) {
                seconds += heightOfTrees[i] - heightOfTrees[i - 1] + 1;
            } else {
                //down
                seconds += heightOfTrees[i - 1] - heightOfTrees[i] + 1;
            }

//            if (heightOfTrees[i] > heightOfTrees[i - 1]) {
//                seconds += heightOfTrees[i] - heightOfTrees[i - 1] + 1;
//            } else {
//                seconds += heightOfTrees[i] + 1;
//            }
            if (i == numberOftrees - 1) {
                break;
            }

            seconds += 1; //when jumping

        }

        System.out.println(seconds);

    }

}