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 squirrel
{
    static class InputReader {
        private InputStream stream;
        private byte[] inbuf = new byte[1024];
        private int start= 0;
        private int end = 0;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        private int readByte() {
            if (start == -1) throw new UnknownError();
            if (end >= start) {
                end= 0;
                try {
                    start= stream.read(inbuf);
                } catch (IOException e) {
                    throw new UnknownError();
                }
                if (start<= 0) return -1;
            }
            return inbuf[end++];
        }

        private boolean isSpaceChar(int c) {
            return !(c >= 33 && c <= 126);
        }

        private int skip() {
            int b;
            while ((b = readByte()) != -1 && isSpaceChar(b)) ;
            return b;
        }

        public String next() {
            int b = skip();
            StringBuilder sb = new StringBuilder();
            while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }

        public int nextInt() {
            int num = 0, b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }

            while (true) {
                if (b >= '0' && b <= '9') {
                    num = num * 10 + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }

        public long nextLong() {
            long num = 0;
            int b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }

            while (true) {
                if (b >= '0' && b <= '9') {
                    num = num * 10 + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }
    }
    public static void main(String args[])
    {
        InputReader sc=new InputReader(System.in);
        int n=sc.nextInt();
        int h[]=new int[n];
        int sum=0;
        for(int i=0;i<n;i++)
        {
            h[i]=sc.nextInt();            
        }
        if(n>=2)
        {
            sum+=h[0]+1;
            if(h[1]<h[0])
                sum+=h[0]-h[1]+1;
            else if(h[1]>h[0])
                sum+=h[1]-h[0]+1;
            else
                sum+=1;
            for(int i=2;i<n;i++)
            {
                if(h[i-1]<h[i])
                {
                    sum+=h[i]-h[i-1]+1;
                }
                else if(h[i-1]>h[i])
                {
                    sum+=h[i-1]-h[i]+1;
                }
                else
                    sum+=1;
            }
            System.out.println(sum+n-1);
        }
        else
            System.out.println(h[0]+1);
    }
}
