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.*;
import java.math.*;
import java.math.BigInteger;
import java.util.LinkedList; 
import java.util.Queue; 
public final class B
{    
    static StringBuilder ans=new StringBuilder();
    static FastReader in=new FastReader();
    static ArrayList<ArrayList<Integer>> g;
    static long mod=1000000007;
    static boolean set[];   

    public static void main(String args[])throws IOException
    {
        int T=i();
        T--;
        long s=i();
        int p=(int)s++;
        while(T-->0)
        {
         int a=i();
         s+=Math.abs(p-a)+2;
         p=a;
         
         
        }
        System.out.println(s);
    }

    static String swap(String X,int i,int j)
    {
        char ch[]=X.toCharArray();
        char a=ch[i];
        ch[i]=ch[j];
        ch[j]=a;
        return new String(ch);
    }

    static int sD(long n)  
    {  

        if (n % 2 == 0 )  
            return 2;  

        for (int i = 3; i * i <= n; i += 2) {  
            if (n % i == 0 )  
                return i;  
        }  

        return (int)n;  
    }  

    static void setGraph(int N)
    {
        set=new boolean[N+1];
        g=new ArrayList<ArrayList<Integer>>();
        for(int i=0; i<=N; i++)
            g.add(new ArrayList<Integer>());
    }

    static void DFS(int N,int d)
    {
        set[N]=true;
        d++;
        for(int i=0; i<g.get(N).size(); i++)
        {
            int c=g.get(N).get(i);
            if(set[c]==false)
            {
                DFS(c,d);
            }
        }
    }

    static  long pow(long a,long b)
    {
        long mod=1000000007;
        long pow=1;
        long x=a;
        while(b!=0)
        {
            if((b&1)!=0)pow=(pow*x)%mod;
            x=(x*x)%mod;
            b/=2;
        }
        return pow;
    }

    static long toggleBits(long x)//one's complement || Toggle bits
    {
        int n=(int)(Math.floor(Math.log(x)/Math.log(2)))+1;

        return ((1<<n)-1)^x;
    }

    static int countBits(long a)
    {
        return (int)(Math.log(a)/Math.log(2)+1);
    }

    static long fact(long N)
    { 
        long n=2; 
        if(N<=1)return 1;
        else
        {
            for(int i=3; i<=N; i++)n=(n*i)%mod;
        }
        return n;
    }

    static int kadane(int A[])
    {
        int lsum=A[0],gsum=A[0];
        for(int i=1; i<A.length; i++)
        {
            lsum=Math.max(lsum+A[i],A[i]);
            gsum=Math.max(gsum,lsum);
        }
        return gsum;
    }

    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 boolean isPrime(long N)
    {
        if (N<=1)  return false; 
        if (N<=3)  return true; 
        if (N%2 == 0 || N%3 == 0) return false; 
        for (int i=5; i*i<=N; i=i+6) 
            if (N%i == 0 || N%(i+2) == 0) 
                return false; 
        return true; 
    }

    static int i()
    {
        return in.nextInt();
    }

    static long l()
    {
        return in.nextLong();
    }

    static int[] input(int N){
        int A[]=new int[N];
        for(int i=0; i<N; i++)
        {
            A[i]=in.nextInt();
        }
        return A;
    }

    static long[] inputLong(int N)     {
        long A[]=new long[N];
        for(int i=0; i<A.length; i++)A[i]=in.nextLong();
        return A;
    }

    static long GCD(long a,long b) 
    {
        if(b==0)
        {
            return a;
        }
        else return GCD(b,a%b );
    }

}
//Code For FastReader
//Code For FastReader
//Code For FastReader
//Code For FastReader
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;
    }

}