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.OutputStream;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.Writer;
import java.math.BigInteger;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author lwc626
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		MyInputReader in = new MyInputReader(inputStream);
		MyOutputWriter out = new MyOutputWriter(outputStream);
		TaskB solver = new TaskB();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskB {
	public void solve(int testNumber, MyInputReader in, MyOutputWriter out) {
        int n = in.nextInt();
        int[] heights = new int[n];
        for(int i = 0; i < n; i ++) heights[i] = in.nextInt();
        int ret = 0;
        int nowAt = 0;
        for(int i = 0; i < n; i ++){
            ret += heights[i] - nowAt + 1;
            if(i > 0) ret += 1;
            if(i < n - 1){
                nowAt = heights[i+1] > heights[i] ? heights[i] : heights[i+1];
                if(heights[i+1] < heights[i])
                    ret += heights[i] - heights[i+1];

            }
        }
        out.printLine(ret);
	}
}

class MyInputReader {

    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;

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

    public int read() {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }

    public int readInt() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }
    public int nextInt(){
        return readInt() ;
    }

    public static boolean isSpaceChar(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    }

class MyOutputWriter {
    private final PrintWriter writer;

    public MyOutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(outputStream);
    }

    public MyOutputWriter(Writer writer) {
        this.writer = new PrintWriter(writer);
    }

    public void print(Object...objects) {
        for (int i = 0; i < objects.length; i++) {
            if (i != 0)
                writer.print(' ');
            writer.print(objects[i]);
        }
    }

    public void printLine(Object...objects) {
        print(objects);
        writer.println();
    }

    public void close() {
        writer.close();
    }

}
