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.StringTokenizer;

public class Roadside_Trees {
    public static void main(String[] args) {
        FastReader in = new FastReader();
        OutputStream outputStream = System.out;
        PrintWriter out = new PrintWriter(outputStream);

        int i,j,a,b,c,n,m;
        long sum = 0;
        n = in.nextInt();
        int[] arr = new int[n+1];

        for (i=1; i<=n; i++){
            arr[i] = in.nextInt();
        }
        if (n == 1) {
            out.print((arr[1] + 1) + "\n");
            out.flush();
            return;
        }


        if (arr[1] >= arr[2]) sum += (arr[1] * 2) - arr[2];
        else sum += arr[1];

        for (i=2; i<=n; i++){

            if (arr[i] >= arr[i-1])
                sum += arr[i] - arr[i-1];
            else
                sum += 0;

            if (i + 1 <= n &&  arr[i] >= arr[i+1]){
                sum += arr[i] - arr[i+1];
            }
            else sum += 0;
        }

        sum += (n*2);
        sum --;

        out.print(sum + " \n");
        out.flush();

    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

}
