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.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.security.KeyStore.Entry;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.Map;
import java.util.StringTokenizer;

public class MainTwo {
    static FastReader in = new FastReader(new BufferedReader(new InputStreamReader(System.in)));
    static PrintWriter out = new PrintWriter(System.out);
    static boolean file = false;
    static final int maxn = (int)1e5 + 11;
    static int inf = (int)1e9;
    static int n,k,m,cnt;
    static ArrayList<Integer> list = new ArrayList<>();
    static int a[] = new int[maxn];
    
    private static void solve() throws Exception {
        int n = in.nextInt();
        for (int i=1; i<=n; i++) {
            a[i] = in.nextInt();
        }
        int ans = a[1]+1;
        for (int i=2; i<=n; i++) {
            ans += Math.abs(a[i-1]-a[i])+2;
        }
        out.println(ans);
    }   


    public static void main (String [] args) throws Exception {
        
        if (file) {
            in = new FastReader(new BufferedReader(new FileReader("input.txt")));
            out = new PrintWriter ("output.txt");
        }
        
        solve();
        out.close();
    }

    


}

class Pair implements Comparable<Pair> {
    int x,y;
    
    public Pair(int x, int y) {
        this.x = x;
        this.y = y;
    }
    @Override
    public boolean equals(Object obj) {
        Pair p = (Pair)obj;
        if (p.x == x && p.y==y) return true;
        return false;
    }
    @Override
    public int hashCode() {
        // TODO Auto-generated method stub
        return x;
    }
    @Override
    public int compareTo(Pair p) {
        if (x<p.x)return 1;
        else if (x==p.x) return 0;
        else return -1;
    }
    
    
    
    
    
}

class FastReader {
    BufferedReader bf;
    StringTokenizer tk = null;

    public FastReader(BufferedReader bf) {
        this.bf = bf;
    }
    
    public String nextToken () throws Exception {
        if (tk==null || !tk.hasMoreTokens()) {
            tk = new StringTokenizer(bf.readLine());
        }
        return tk.nextToken();
    }
    
    public int nextInt() throws Exception {
        return Integer.parseInt(nextToken());
    }
    
    public long nextLong() throws Exception {
        return Long.parseLong(nextToken());
    }
    
    public double nextDouble() throws Exception {
        return Double.parseDouble(nextToken());
    }
}