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.lang.reflect.Array;
import java.util.*;

public class Main {
    private void solve() throws Exception{
        int n = ri();
        int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = ri();
        int count = a[0];
        for (int i = 1; i < n; i++){
            if (a[i] > a[i-1]) count += a[i]-a[i-1]+1;
            else if (a[i] < a[i-1]) count += a[i-1]-a[i]+1;
            else count++;
        }
        println(""+(count+n));
        out.close();
    }

    public static void main(String[] args) throws Exception{
        Main m = new Main();
        m.solve();
    }


    /* Template Methods */
    private BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
    private BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
    //private PrintWriter out = new PrintWriter(System.out, true);
    private StringTokenizer st;
    /* console write methods */
    private void print(String s) throws  Exception{
        out.write(s);
    }
    private void println(String s) throws Exception{
        out.write(s);
        out.newLine();
    }

    /* console read methods */
    private String rs() throws IOException{
        return in.readLine();
    }
    private int ri() throws IOException{
        return Integer.parseInt(rs());
    }
    private float rf() throws  IOException{
        return Float.parseFloat(rs());
    }
    private double rd() throws IOException{
        return Double.parseDouble(rs());
    }
    private int[] ria(int size) throws IOException{
        int[] a = new int[size];
        st = new StringTokenizer(rs(), " ");
        int i = 0;
        while(st.hasMoreTokens()){ a[i] = Integer.parseInt(st.nextToken()); i++; }
        return a;
    }
    private long[] rla(int size) throws IOException{
        long[] a = new long[size];
        st = new StringTokenizer(rs(), " ");
        int i = 0;
        while(st.hasMoreTokens()){ a[i] = Long.parseLong(st.nextToken()); i++; }
        return a;
    }
    private ArrayList ral() throws IOException{
        ArrayList al = new ArrayList();
        st = new StringTokenizer(rs(), " ");
        while(st.hasMoreTokens()) al.add(st.nextToken());
        return al;
    }
    /* MAX & MIN */
    private int max(int[] a){
        int max = Integer.MIN_VALUE;
        for (int x: a) if (x > max) max = x;
        return max;
    }
    private int min(int[] a){
        int min = Integer.MAX_VALUE;
        for (int x: a) if (x < min) min = x;
        return min;
    }
}