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.*;
import java.io.*;

public class File {
	public static class FastScanner {
		BufferedReader br;
		StringTokenizer st;
		
		public FastScanner() {
			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());
		}
	}
	
	public static void main(String[] args) {
		FastScanner sc = new FastScanner();
		PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
		
		
		
		
		int n = sc.nextInt();
		int[] h = new int[n];
		
		for (int i = 0; i < n; i++) {
			h[i] = sc.nextInt();
		}
		
		int currHeight = 0;
		int res = 0;
		
		for (int i = 0; i < n; i++) {
			// Move to top of current tree and eat nut.
			res += (h[i] - currHeight);
			currHeight = h[i];
			res++;
			
			// Jump to next tree, if any
			if (i + 1 < n) {
				// Move down to height of next tree if next is shorter.
				if (h[i+1] < h[i]) {
					res += (h[i] - h[i+1]);
					currHeight = h[i+1];
				}
				
				res++; // Jump to next tree.
			}
		}
		
		out.println(res);
		
		out.close();
	}
}






















