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.*;
import java.util.ArrayList;
import java.util.Scanner;

public class B162 {

    public void solve() throws IOException {
        Scanner sc = new Scanner(System.in);
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));


        int i = 0, j = 0;
        int n = sc.nextInt();
        int a[] = new int[n];

        for (i = 0; i < n; ++i) {
            a[i] = sc.nextInt();
        }
        int sum = a[0] + 1 + 1;//h+eat+jump
        if(n==1){
            sum--;
        }
        for (i = 1; i < n; ++i) {
            if (i == n - 1) {
                if (a[i] < a[i - 1]) {
                    sum += 1+a[i-1]-a[i];
                } else {
                    sum += (1 + a[i] - a[i - 1]);
                }
            } else {
                if (a[i] <= a[i - 1]) {
                    sum += 2+a[i-1]-a[i];
                } else {
                    sum += (2 + a[i] - a[i - 1]);
                }
            }
        }

        System.out.println(sum);
    }

    public static void main(String[] args) throws IOException {
        new B162().solve();
    }
}
