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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

public class B implements Runnable {

	public static void main(String[] args) throws Exception {

		new Thread(null, new B(), "SwapnilGanguly", 1 << 26).start();
	}

	public void run() {

		MyScanner sc = new MyScanner();
		PrintWriter pr = new PrintWriter(System.out);

		int T = 1;

		while (T-- > 0) {

			int n = sc.nextInt();
			int[] ar = sc.readArray(n);

			long ans = ar[0];
			for (int i = 1; i < n; i++)
				ans += Math.abs(ar[i] - ar[i - 1]);

			ans += (n << 1) - 1;
			pr.println(ans);
		}

		pr.close();
	}

	public static void sort(int[] a) {

		ArrayList<Integer> l = new ArrayList<>();

		for (int i : a)
			l.add(i);

		Collections.sort(l);

		for (int i = 0; i < a.length; i++)
			a[i] = l.get(i);
	}

	public static class MyScanner {
		BufferedReader br;
		StringTokenizer st;

		public MyScanner() {
			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;
		}

		int[] readArray(int n) {

			int[] ar = new int[n];

			for (int i = 0; i < n; i++)
				ar[i] = nextInt();

			return ar;
		}
	}
}


