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 B {
	
	public static void main(String[] args) {
		FastScanner sc = new FastScanner();
		int n = sc.nextInt();
		
		int[] arr = new int[n];
		
		for(int i = 0; i < n; i++) {
			arr[i] = sc.nextInt();
		}
		
		int count = arr[0] + 1;
		
		for(int i = 0; i < n-1; i++) {
			if(arr[i] > arr[i+1]) {
				count += arr[i]-arr[i+1];
				count++;
				count++;
			}
			else {
				count++;
				count += arr[i+1] - arr[i];
				count++;
			}
		}
		
		
		System.out.println(count);
			
		
				
		
		
	} 


	


	


	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}
	
	
	
	
	static int gcd(int a, int b) {
		return a%b == 0 ? b : gcd(b,a%b);
	}
	
	static boolean[] sieve(int n) {
		
		boolean isPrime[] = new boolean[n+1];
		for(int i = 2; i <= n; i++) {
			if(isPrime[i]) continue;
			for(int j = 2*i; j <= n; j+=i) {
				isPrime[j] = true;
			}
		
		}
		return isPrime;
		
	}
}
