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.awt.Point;
import java.io.BufferedReader;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.List;
import java.util.Scanner;
import java.util.Set;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class B {

    public static void main(String[] Args) throws IOException {
        new B().solve();
    }

    static int[] dx_ = { 0, 0, 1, -1 };
    static int[] dy_ = { 1, -1, 0, 0 };

    ArrayList<Integer>[] graph;

    int k = 0;

    // DISCUSS TIME LIMIT EXCEEDED!!!! PROPER DATA STRUCTURE!!!
    // Use array if possible or the most efficient data structure
    void solve() throws IOException {
        int n = si(), a[] = si(n), o = 0, h = 0;

        for (int i = 0; i < n; i++) {
            o += (a[i] - h) + 1; // move and eat
            h = a[i];
            if (i + 1 < n) {
                if (h > a[i + 1]) {
                    o += (h - a[i + 1]);
                    h = a[i + 1];
                }
                o++;
            }
        }
        System.out.println(o);

    }

    public boolean equals(LinkedList<Integer> o1, LinkedList<Integer> o2) {
        // TODO Auto-generated method stub
        if (o1.size() != o2.size())
            return false;
        else {
            LinkedList<Integer> o = new LinkedList<Integer>();
            o.addAll(o1);
            o.removeAll(o2);
            return o.size() == 0;
        }
    }

    LinkedList<Integer> path = new LinkedList<Integer>();
    ArrayList<LinkedList<Integer>> cycles = new ArrayList<LinkedList<Integer>>();

    void dfs(int now, int[] v) {
        v[now] = 1;
        path.addLast(now);
        for (int to : graph[now]) {
            if (v[to] == 0)
                dfs(to, v);
        }
        if (path.size() > 2)
            if (graph[path.getLast()].contains(path.getFirst())) {
                add(path);
            }

        path.removeLast();
    }

    void add(LinkedList<Integer> b) {
        for (LinkedList<Integer> a : cycles) {
            if (equals(a, b))
                return;
        }
        cycles.add((LinkedList<Integer>) b.clone());
    }

    // ----------------------- Library ------------------------

    // ----------------------- GRAPH ------------------------

    /**
     * important for speed!!! PrintWriter out=new PrintWriter(new
     * OutputStreamWriter(System.out)); out.print(...); out.close();
     * 
     * @param v
     */
    // leap year is 29
    int[] year = { 0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 };

    void initSystem() throws IOException {
        if (br != null)
            br.close();
        br = new BufferedReader(new InputStreamReader(System.in));
    }

    void initFile() throws IOException {
        if (br != null)
            br.close();
        br = new BufferedReader(new InputStreamReader(new FileInputStream(
                "input.txt")));
    }

    void printWriter() {
        try {
            PrintWriter pr = new PrintWriter("output.txt");
            pr.println("hello world");
            pr.close();
        } catch (FileNotFoundException e) {
            // TODO Auto-generated catch block
            e.printStackTrace();
        }
    }

    void comparator() {
        Point[] v = new Point[10];
        Arrays.sort(v, new Comparator<Point>() {
            @Override
            public int compare(Point a, Point b) {
                if (a.x != b.x)
                    return -(a.x - b.x);
                return a.y - b.y;
            }
        });
    }

    double distance(Point a, Point b) {
        double dx = a.x - b.x, dy = a.y - b.y;
        return Math.sqrt(dx * dx + dy * dy);
    }

    Scanner in = new Scanner(System.in);

    String ss() {
        return in.next();
    }

    String sline() {
        return in.nextLine();
    }

    int si() {
        return in.nextInt();
    }

    long sl() {
        return in.nextLong();
    }

    int[] sai(int n) {
        int[] a = new int[n];
        for (int i = 0; i < a.length; i++) {
            a[i] = in.nextInt();
        }
        return a;
    }

    int[] si(int n) {
        int[] a = new int[n];
        for (int i = 0; i < a.length; i++) {
            a[i] = in.nextInt();
        }
        return a;
    }

    String[] ss(int n) {
        String[] a = new String[n];
        for (int i = 0; i < a.length; i++) {
            a[i] = ss();
        }
        return a;
    }

    int[] sai_(int n) {
        int[] a = new int[n + 1];
        for (int i = 1; i <= n; i++) {
            a[i] = in.nextInt();
        }
        return a;
    }

    BufferedReader br;
    StringTokenizer tokenizer;
    {
        br = new BufferedReader(new InputStreamReader(System.in));
    }

    void tok() throws IOException {
        tokenizer = new StringTokenizer(br.readLine());
    }

    int toki() throws IOException {

        return Integer.parseInt(tokenizer.nextToken());
    }

    int[] rint(int n) throws IOException {
        int[] a = new int[n];
        for (int i = 0; i < a.length; i++)
            a[i] = Integer.parseInt(tokenizer.nextToken());

        return a;
    }

    int[] rint_(int n) throws IOException {
        int[] a = new int[n + 1];
        for (int i = 1; i <= n; i++)
            a[i] = Integer.parseInt(tokenizer.nextToken());

        return a;
    }

    String[] rstrlines(int n) throws IOException {
        String[] a = new String[n];
        for (int i = 0; i < n; i++) {
            a[i] = br.readLine();
        }
        return a;
    }

    long tokl() {
        return Long.parseLong(tokenizer.nextToken());
    }

    double tokd() {
        return Double.parseDouble(tokenizer.nextToken());
    }

    String toks() {
        return tokenizer.nextToken();
    }

    String rline() throws IOException {
        return br.readLine();
    }

    List<Integer> toList(int[] a) {
        List<Integer> v = new ArrayList<Integer>();
        for (int i : a)
            v.add(i);
        return v;
    }

    static void pai(int[] a) {
        System.out.println(Arrays.toString(a));
    }

    static int toi(Object s) {
        return Integer.parseInt(s.toString());
    }

    static int[] dx3 = { 1, -1, 0, 0, 0, 0 };
    static int[] dy3 = { 0, 0, 1, -1, 0, 0 };
    static int[] dz3 = { 0, 0, 0, 0, 1, -1 };

    static int[] dx = { 1, 0, -1, 1, -1, 1, 0, -1 }, dy = { 1, 1, 1, 0, 0, -1,
            -1, -1 };

    static int INF = 2147483647; // =2^31-1 // -8
    static long LINF = 922337203854775807L; // -8
    static short SINF = 32767; // -32768

    // finds GCD of a and b using Euclidian algorithm
    public int GCD(int a, int b) {
        if (b == 0)
            return a;
        return GCD(b, a % b);
    }

    static List<String> toList(String[] a) {
        return Arrays.asList(a);
    }

    static String[] toArray(List<String> a) {
        String[] o = new String[a.size()];
        a.toArray(o);
        return o;
    }

    static int[] pair(int... a) {
        return a;
    }
}
