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.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.Writer;
import java.util.InputMismatchException;

public class RoadSideTrees {
    public static void main(String[] args) {
    InputReader in = new InputReader(System.in);
    OutputWriter out = new OutputWriter(System.out);
    int n = in.readInt();
    int[] h = new int[n];
    int ch = 0;
    long sum = 0;
    for (int i = 0; i < n; i++) {
        h[i] = in.readInt();
    }
    for (int i = 0; i < n; i++) {
        if (ch < h[i]) {
        sum += h[i] - ch;// climb
        }
        sum += 1;// eat
        ch = h[i];
        if (i != n - 1 && ch > h[i + 1]) {
        sum += ch - h[i + 1];// down
        ch = h[i + 1];
        }
        if (i != n - 1)
        sum += 1;// jump
    }
    out.print(sum);
    out.close();
    }

    static class InputReader {
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;

    public InputReader(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 String readLine() {
        int c = read();
        while (isSpaceChar(c))
        c = read();
        StringBuilder res = new StringBuilder();
        do {
        res.appendCodePoint(c);
        c = read();
        } while (!isEndOfLine(c));
        return res.toString();
    }

    public String readString() {
        int c = read();
        while (isSpaceChar(c))
        c = read();
        StringBuilder res = new StringBuilder();
        do {
        res.appendCodePoint(c);
        c = read();
        } while (!isSpaceChar(c));
        return res.toString();
    }

    public long readLong() {
        int c = read();
        while (isSpaceChar(c))
        c = read();
        int sgn = 1;
        if (c == '-') {
        sgn = -1;
        c = read();
        }
        long 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 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 boolean isSpaceChar(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    public boolean isEndOfLine(int c) {
        return c == '\n' || c == '\r' || c == -1;
    }
    }

    static class OutputWriter {
    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(
            outputStream)));
    }

    public OutputWriter(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();
    }
    }
}
