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.*;

public class A
{
	public static void main(String[] args) throws IOException {
		Scanner sc=new Scanner(System.in);
		PrintWriter pw=new PrintWriter(System.out);
		int n=sc.nextInt();
		int []h=new int [n];
		for(int i=0;i<n;i++)
			h[i]=sc.nextInt();
		int ans=n+h[0]+n-1;
		for(int i=1;i<n;i++)
			ans+=Math.abs(h[i]-h[i-1]);
			
			
		
				
		
		
		
		
		pw.println(ans);
		pw.close();
		
		
	}
	
	
	
	
	static class Scanner
	{
	StringTokenizer st;
	BufferedReader br;

	public Scanner(InputStream s) {
		br = new BufferedReader(new InputStreamReader(s));
	}
	public String next() throws IOException {
		while (st == null || !st.hasMoreTokens())
			st = new StringTokenizer(br.readLine());
		return st.nextToken();
	}
	public Scanner(String s) throws FileNotFoundException {
		br = new BufferedReader(new FileReader(s));
	}
	public int nextInt() throws IOException {
		return Integer.parseInt(next());
	}
	public double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}

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

	public String nextLine() throws IOException {
		return br.readLine();
	}

	public boolean ready() throws IOException {
		return br.ready();
	}
}

}