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.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Solution {
	
	public void solve() throws IOException {
		int n = in.nextInt(), ans = 0, prev = 0;
		
		for (int i = 0; i < n; ++i) {
			int h = in.nextInt();
			ans += Math.abs(h - prev) + 2;
			prev = h;
		}
		ans--;
		
		System.out.println(ans);
	}
	
	public void run() throws IOException {
		in = new MyScanner();
		solve();
		in.close();
	}
	
	private MyScanner in;
	//private PrintWriter out;
	
	public class MyScanner {
		private BufferedReader br;
		private StringTokenizer st;
		
		public MyScanner() {
			this.br = new BufferedReader(new InputStreamReader(System.in));
		}
		
		public MyScanner(String fileTitle) throws IOException {
			this.br = new BufferedReader(new FileReader(fileTitle + ".in"));
		}
		
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens()) {
				String s = br.readLine();
				if (s == null) {
					return "-1";
				}
				st = new StringTokenizer(s);
			}
			return st.nextToken();
		}
		
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
		
		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
		
		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
		
		public int[] nextIntArray(int size) throws IOException {
			int[] arr = new int[size];
			for (int i = 0; i < size; ++i) {
				arr[i] = nextInt();
			}
			return arr;
		}
		
		public void close() throws IOException {
			br.close();
		}
	}
	
	public static void main(String[] args) throws IOException {
		new Solution().run();
	}

}
