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.util.Scanner;
import java.io.*;
import javax.lang.model.util.ElementScanner6; 

public class B265
{

    public static void main(String args[])
    {  

        FastReader in=new FastReader();
        PrintWriter pr = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        int t=1;
     
        //t=in.nextInt();
        while(t-->0)
        {
          
            int n=in.nextInt();
            int arr[]=new int[n];
            for(int i=0;i<n;i++)
            {
                arr[i]=in.nextInt();

            }

            int count=0;
            int place=0;
            for(int i=0;i<n-1;i++)
            {
                count+=arr[i]-place+1;
                if(arr[i]<=arr[i+1])
                {
                    place=arr[i];
                    count++;
                }
                else
                {
                    place=arr[i+1];
                    count+=1+arr[i]-arr[i+1];
                }
            }
            count+=arr[n-1]-place+1;
            pr.println(count);
        
        }
        pr.flush();
    }



    
    static int gcd(int a,int b)
    {
        
        if(a==0)
            return b;
        return gcd(a%b,b);
    }

    static int lcm(int a,int b)
    {
        return (a*b)/gcd(a,b);
    }


    static boolean prime[];

    static void sieveofe()
    {
        int n=1000000;
      
        prime=new boolean[n+1];
        Arrays.fill(prime,true);
        prime[1]=false;
        for(int i=2;i*i<=n;i++)
        {
            if(prime[i]==true)
            {
                for(int j=i*i;j<=n;j+=i)
                {
                    prime[j]=false;
                }
            }
        }
      
        
    }
    
    static void sort(long[] a) {
		ArrayList<Long> l = new ArrayList<>();
		for (long i : a)
			l.add(i);
		Collections.sort(l);
		for (int i = 0; i < a.length; i++)
			a[i] = l.get(i);
	}
    
    
	static void sort(int[] a) {
		ArrayList<Integer> l = new ArrayList<>();
		for (int i : a)
			l.add(i);
		Collections.sort(l);
		for (int i = 0; i < a.length; i++)
			a[i] = l.get(i);
    }

    
    static class FastReader
    { 
        BufferedReader br; 
        StringTokenizer st; 

        public FastReader() 
        { 
            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; 
        } 
    } 

    
   
}