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.InputStreamReader;
import java.util.StringTokenizer;

public class B {
	static BufferedReader stdin = new BufferedReader(new
			InputStreamReader(System.in));
	static StringTokenizer st = new StringTokenizer("");
	public static void main(String[] args) throws Exception {
		int N = readInt();
		int[] h = new int[N];
		for (int i = 0; i < N; i++)
			h[i] = readInt();
		int i = 0, nuts = 0;
		int y = 0, t = 0;
		do {
			while (y < h[i]) {y++; t++;}
			nuts++; t++;
			if (nuts == N) {
				System.out.println(t);
				return;
			}
			while (h[i+1] < y) {y--; t++;}
			i++; t++;
		} while (true);
	}
	
	static String readString() throws Exception {
		while (!st.hasMoreTokens()) {
			st = new StringTokenizer(stdin.readLine());
		}
		return st.nextToken();
	}
	
	static int readInt() throws Exception {
		return Integer.parseInt(readString());
	}
	
	static long readLong() throws Exception {
		return Long.parseLong(readString());
	}
	
	static double readDouble() throws Exception {
		return Double.parseDouble(readString());
	}
}
