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.*;

public class Main {
	
	public static void main(String[] args) throws Exception {
		
		int n = nextInt();
		int[] h = new int[n];
		for(int i = 0; i < n; i++){
			h[i] = nextInt();
		}
		int time = 0;
		int ch = 0;
		for(int i = 0; i < n; i++){
			if(i == 0){
				ch += h[i];
				time += h[i] + 1;
			} else {
				if(ch >= h[i]){
					time++;
					time += ch - h[i] + 1;
					ch -= ch - h[i];
				} else {
					time++;
					time += h[i] - ch + 1;
					ch += h[i] - ch;
				}
			}
			
		}
		println(time);
		
		
	}
	
	private static PrintWriter out =  new PrintWriter(System.out);
	private static BufferedReader inB = new BufferedReader(new InputStreamReader(System.in));	
	private static StreamTokenizer in = new StreamTokenizer(inB);
	
	private static void exit(Object o) throws Exception {
		out.println(o);
		out.flush();
		System.exit(0);
	}
	private static void println(Object o) throws Exception{
		out.println(o);
		out.flush();
	}
	private static void print(Object o) throws Exception{
		out.print(o);
		out.flush();
	}
	private static int nextInt() throws Exception {
		in.nextToken();
		return (int)in.nval;
	}  
	private static String nextString() throws Exception {
		in.nextToken();
		return in.sval;        
	}
	
} 