Little Petya loves training spiders. Petya has a board n × m in size. Each cell of the board initially has a spider sitting on it. After one second Petya chooses a certain action for each spider, and all of them humbly perform its commands. There are 5 possible commands: to stay idle or to move from current cell to some of the four side-neighboring cells (that is, one command for each of the four possible directions). Petya gives the commands so that no spider leaves the field. It is allowed for spiders to pass through each other when they crawl towards each other in opposite directions. All spiders crawl simultaneously and several spiders may end up in one cell. Petya wants to know the maximum possible number of spider-free cells after one second.

Input

The first line contains two space-separated integers n and m (1 ≤ n, m ≤ 40, n·m ≤ 40) — the board sizes.

Output

In the first line print the maximum number of cells without spiders.

Examples

Input

1 1


Output

0


Input

2 3


Output

4

Note

In the first sample the only possible answer is:

s

In the second sample one of the possible solutions is: 
    
    
      
    rdl  
    rul  
    

s denotes command "stay idle", l, r, d, u denote commands "crawl left", "crawl right", "crawl down", "crawl up", correspondingly.
import java.util.ArrayList;
import java.util.List;
import java.util.InputMismatchException;
import java.math.BigInteger;
import java.util.Iterator;
import java.io.*;
import java.util.Comparator;
import java.util.Arrays;
import java.util.Collection;

/**
 * Generated by Contest helper plug-in
 * Actual solution is at the bottom
 */
public class Main {
	public static void main(String[] args) {
		InputReader in = new StreamInputReader(System.in);
		PrintWriter out = new PrintWriter(System.out);
		run(in, out);
	}

	public static void run(InputReader in, PrintWriter out) {
		Solver solver = new TaskC();
		solver.solve(1, in, out);
		Exit.exit(in, out);
	}
}

abstract class InputReader {
	private boolean finished = false;

	public abstract int read();

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

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

	public void setFinished(boolean finished) {
		this.finished = finished;
	}

	public abstract void close();
}

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

	public StreamInputReader(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 void close() {
		try {
			stream.close();
		} catch (IOException ignored) {
		}
	}
}

class Exit {
	private Exit() {
	}

	public static void exit(InputReader in, PrintWriter out) {
		in.setFinished(true);
		in.close();
		out.close();
	}
}

interface Solver {
	public void solve(int testNumber, InputReader in, PrintWriter out);
}

class ArrayUtils {

	public static void fill(int[][] array, int value) {
		for (int[] row : array)
			Arrays.fill(row, value);
	}

	public static void fill(int[][][] array, int value) {
		for (int[][] subArray : array)
			fill(subArray, value);
	}

	}

class TaskC implements Solver {
	public void solve(int testNumber, InputReader in, PrintWriter out) {
		int rowCount = in.readInt();
		int columnCount = in.readInt();
		out.println(rowCount * columnCount - go(Math.min(rowCount, columnCount), Math.max(rowCount, columnCount)));
	}

	private int go(int rowCount, int columnCount) {
		int[][][] result = new int[columnCount][rowCount][1 << (2 * rowCount)];
		ArrayUtils.fill(result, -1);
		return go(0, 0, (1 << rowCount) - 1, result);
	}

	private int go(int column, int row, int mask, int[][][] result) {
		if (column == result.length)
			return (mask == 0 ? 0 : Integer.MAX_VALUE / 2);
		int length = result[column].length;
		if (row == length)
			return go(column + 1, 0, mask, result);
		if (result[column][row][mask] != -1)
			return result[column][row][mask];
		result[column][row][mask] = Integer.MAX_VALUE / 2;
		if ((mask >> (2 * length - 1) & 1) == 0)
			result[column][row][mask] = go(column, row + 1, mask * 2 + (column == result.length - 1 ? 0 : 1), result);
		int newMask = mask;
		newMask &= ~(1 << (length - 1));
		if (row != 0)
			newMask &= ~(1 << length);
		if (row != length - 1)
			newMask &= ~(1 << (length - 2));
		newMask *= 2;
		newMask &= (1 << (2 * length)) - 1;
		return result[column][row][mask] = Math.min(result[column][row][mask], 1 + go(column, row + 1, newMask, result));
	}
}

