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


public class RoadSideTrees {

	static int[] tree;
	static int N;
	static int t = 0;
	public static void main(String[]args){
		IR2 in = new IR2(System.in);
		N = in.i();
		tree = new int[N];
		for(int i=0;i<N;i++) tree[i] = in.i();
		int h = 0;
		for(int i=0;i<N;i++){
			t += tree[i]-h+1; 
			h = tree[i];
			if(i+1<N){
				if(tree[i+1]>h) {
					t += (tree[i+1]-h);
					h = tree[i+1];
					t++;
				}
				else{
					t += tree[i]-tree[i+1];
					t++;
					h = tree[i+1];
				}
			}
			
		}
		System.out.print(t);
	}
}


class IR2 {
	public BufferedReader reader;
	public StringTokenizer tokenizer;

	public IR2(InputStream stream) {
		reader = new BufferedReader(new InputStreamReader(stream), 32768);
		tokenizer = null;
	}

	public String next() {
		while (tokenizer == null || !tokenizer.hasMoreTokens()) {
			try {
				tokenizer = new StringTokenizer(reader.readLine());
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return tokenizer.nextToken();
	}

	public int i() {
		return Integer.parseInt(next());
	}

}