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.math.*;
import java.security.*;
import java.text.*;
import java.util.*;
import java.util.concurrent.*;
import java.util.regex.*;
import java.util.Arrays;
import java.util.ArrayList;
import java.lang.Math; 
 
 
 
public class project 
{ 
    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; 
        } 
    } 

   

    static int binarySearch(int a[],int k,int l,int h){
        
        while(l<=h){
         int mid = (l+h)/2;
         if(a[mid]==k) return mid;
         else if(a[mid]>k) h=mid-1;
         else if(a[mid]<k) l =mid+1;
    }
        
        return -1;
    }



    static String reverse(String input)  
    { 
        char[] a = input.toCharArray(); 
        int l, r = 0; 
        r = a.length - 1; 
  
        for (l = 0; l < r; l++, r--) 
        { 
            // Swap values of l and r  
            char temp = a[l]; 
            a[l] = a[r]; 
            a[r] = temp; 
        } 
        return String.valueOf(a); 
    } 

   
    
    static int gcd(int a, int b) 
    { 
        // Everything divides 0  
        if (a == 0) 
          return b; 
        if (b == 0) 
          return a; 
       if (a == b) 
            return a; 
       if (a > b) 
            return gcd(a-b, b); 
        return gcd(a, b-a); 
    } 

    static int solve(int A, int B) 
   { 
    int count = 0; 
    for (int i = 0; i < 21; i++) { 
        if (((A >> i) & 1) != ((B >> i) & 1)) { 
            count++; 
        } 
    } 
  
   return count;
  } 

        static long nCr(int n, int r) 
        { 
            return fact(n) / (fact(r) * 
                        fact(n - r)); 
        } 
        
        
        static long fact(int n) 
        { 
            long res = 1; 
            for (int i = 2; i <= n; i++) 
                res = res * i; 
            return res; 
        } 
        
        public static long count(long k) {
            return k * (k - 1) / 2;
        }

        static boolean isPrime(int n) { 
            // if(n==1) return false; 
            if(n==2) return true;
            if (n%2==0) return false; 
            
            for(int i=3;i<=Math.sqrt(n);i+=2) { 
                if(n%i==0) 
                    return false; 
            } 
            return true; 
        }

        static int negMod(int n){
            int a = (n % 1000000007 + 1000000007) % 1000000007;
            return a;
        }
        
        public static void main(String[] args) throws Exception 
    {   
       
        OutputStream outputStream = System.out;
        PrintWriter w = new PrintWriter(outputStream);
        FastReader sc = new FastReader();
        // Scanner sc = new Scanner(new File("input.txt"));
        // PrintWriter out = new PrintWriter(new File("output.txt"));
        int i,j;
        
        int n = sc.nextInt();
        int a[] = new int[n];

        for(i=0;i<n;i++)  a[i] = sc.nextInt();
        long min = 0;
        min += a[0]+1;
        int s = 0;
        for(i=1;i<n;i++){
            if(a[i]<a[i-1]){
              s = a[i-1] - a[i];
              min += s + 2;
            }
            else if(a[i]>=a[i-1]){
             s = a[i] - a[i-1];
             min += s+2; 
            }
        }
        w.print(min);
        w.close();
     }

       
}




// System.out.println();

        
    
    

