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;

/**
 * Created by hossam on 3/2/17.
 */


public class Main {

    public static void main(String[] args) {

        int time = 0;

        Scanner scanner = new Scanner(System.in);

        int numberTrees = scanner.nextInt();

        int[] height = new int[numberTrees];

        for (int s = 0; s < numberTrees; s++) {

            height[s] = scanner.nextInt();
        }

        for (int i = 0; i < numberTrees; i++) {

            if (i == 0 && i != numberTrees - 1) {
                time = time + 2 + height[i];
            } else if (i == 0 && i == numberTrees - 1) {
                time = time + 1 + height[i];
            } else {
                for (int s = i - 1; s < i; s++) {

                    if (height[s] > height[i] && i != numberTrees - 1) {

                        time = time + 2 + height[s] - height[i];

                    } else if (height[s] > height[i] && i == numberTrees - 1) {

                        time = time + 1 + height[s] - height[i];

                    } else if (height[s] < height[i] && i != numberTrees - 1) {

                        time = time + 2 + height[i] - height[s];

                    } else if (height[s] < height[i] && i == numberTrees - 1) {

                        time = time + 1 + height[i] - height[s];

                    } else if (height[i] == height[s] && i != numberTrees - 1) {

                        time = time + 2;

                    } else if (height[i] == height[s] && i == numberTrees - 1) {

                        time = time + 1;
                    }


                }
            }
        }


        System.out.println(time);
    }

}

