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.util.*;
import java.io.*;

public class Solve {
	public static void main(String[] args){
		FastScanner sc = new FastScanner();
    int n = sc.nextInt();
    int[] h = new int[n];

    for(int i=0; i<n; i++){
      h[i] = sc.nextInt();
    }

    int current = 0;
    int count = 0;
    for(int i=0; i<n-1; i++){
      count += h[i]-current+1;
      if(h[i+1]>=h[i]){
        count++;
        current = h[i];
      } else{
        count += h[i]-h[i+1]+1;
        current = h[i+1];
      }
    }

    count += h[n-1]-current+1;

    System.out.println(count);
	}

	public static class FastScanner {
      BufferedReader br;
      StringTokenizer st;
 
      public FastScanner(){
         br = new BufferedReader(new InputStreamReader(System.in));
      }
 
      String next(){
          while (st == null || !st.hasMoreElements()) {
              try {
                  st = new StringTokenizer(br.readLine());
              } catch (IOException e) {
                  e.printStackTrace();
              }
          }
          return st.nextToken();
      }
 
      int nextInt(){
          return Integer.parseInt(next());
      }
 
      long nextLong(){
          return Long.parseLong(next());
      }
 
      double nextDouble(){
          return Double.parseDouble(next());
      }
 
      String nextLine(){
      	String str = "";
    		try {
    			str = br.readLine();
    		} catch (IOException e) {
    			e.printStackTrace();
    		}
    		return str;
      }
   }
}