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.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import static java.lang.Math.*;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Map.Entry;
import java.util.StringTokenizer;
import java.util.TreeMap;

/**
 *
 * @author pttrung
 */
public class C {

    public static double Epsilon = 1e-6;
    public static long x, y, d;
    public static long MOD = 1000000007;
    public static int[][][] dp;
    public static int min, max, need;

    public static void main(String[] args) {

        Scanner in = new Scanner();
        PrintWriter out = new PrintWriter(System.out);

        int n = in.nextInt();
        int m = in.nextInt();
        min = Math.min(n, m);
        max = (m + n) - min;
        dp = new int[max][1 << min][1 << min];

        for (int[][] temp : dp) {
            for (int[] val : temp) {
                Arrays.fill(val, -1);
            }
        }
        need = (1 << min) - 1;
        //System.out.println(add + total);
        //  System.out.println(min + " " + max);

        out.println(cal(0, 0, 0));

        out.close();

    }

    public static int cal(int index, int last, int lastHold) {

        if (index == max) {
            return 0;
        }
        if (dp[index][lastHold][last] != -1) {
            return dp[index][lastHold][last];
        }
        int result = 0;

        for (int i = 0; i < 1 << min; i++) {
            if ((i | last) == need || (index == 0)) {
              //  System.out.println("PREV " + index + " " + i + " " + last + " " + lastHold);
              //  System.out.println("NEXT " + index + " " + i + " " + (i | lastHold) + " " + i);
                //   System.out.println(Integer.bitCount(i) + " " + i);

//                if (index == 3) {
//                    System.out.println(last + " " + i + " " + match(i, last) + " " + next);
//                }
                if(index + 1 == max && match(i,lastHold)!= need){
                    continue;
                }
                int temp = cal(index + 1, match(i,lastHold), i) + (min - Integer.bitCount(i));
                result = result < temp ? temp : result;

                //  break;
            }
        }
        dp[index][lastHold][last] = result;
        return result;
    }

    public static int match(int mask, int last) {
        int result = last;
        for (int i = 0; i < min; i++) {
            if (((1 << i) & mask) != 0) {
                int a = i - 1;
                int b = i + 1;
                result |= (1 << i);
                if (a >= 0) {
                    result |= (1 << a);
                }
                if (b < min) {
                    result |= (1 << b);
                }
            }
        }
        // System.out.println(mask + " " + result + " " + need);
        return result ;
    }

    public static long pow(long a, long b) {
        if (b == 0) {
            return 1;
        }
        long val = pow(a, b / 2);
        if (b % 2 == 0) {
            return val * val % MOD;
        } else {
            return a * (val * val % MOD) % MOD;
        }
    }

    public static void extendEuclid(long a, long b) {
        if (b == 0) {
            x = 1;
            y = 0;
            d = a;
            return;
        }
        extendEuclid(b, a % b);
        long x1 = y;
        long y1 = x - (a / b) * y;
        x = x1;
        y = y1;

    }

    public static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    static class Line {

        double a, b, c;

        Line(double x1, double y1, double x2, double y2) {
            if (Math.abs(x1 - x2) < Epsilon && Math.abs(y1 - y2) < Epsilon) {
                throw new RuntimeException("Two point are the same");
            }
            a = y1 - y2;
            b = x2 - x1;
            c = -a * x1 - b * y1;
        }

        Line(Point x, Point y) {
            this(x.x, x.y, y.x, y.y);
        }

        public Line perpendicular(Point p) {
            return new Line(p, new Point(p.x + a, p.y + b));
        }

        public Point intersect(Line l) {
            double d = a * l.b - b * l.a;
            if (d == 0) {
                throw new RuntimeException("Two lines are parallel");
            }

            return new Point((l.c * b - c * l.b) / d, (l.a * c - l.c * a) / d);
        }
    }

    static void check(Point a, Point b, ArrayList<Point> p, Point[] rec, int index) {
        for (int i = 0; i < 4; i++) {
            int m = (i + index) % 4;
            int j = (i + 1 + index) % 4;
            Point k = intersect(minus(b, a), minus(rec[m], rec[j]), minus(rec[m], a));
            if (k.x >= 0 && k.x <= 1 && k.y >= 0 && k.y <= 1) {
                Point val = new Point(k.x * minus(b, a).x, k.x * minus(b, a).y);
                p.add(add(val, a));
                // System.out.println(a + " " + b + " " + rec[i] + " " + rec[j]);
                // System.out.println(add(val, a));
            }
        }
    }

    static Point intersect(Point a, Point b, Point c) {
        double D = cross(a, b);
        if (D != 0) {
            return new Point(cross(c, b) / D, cross(a, c) / D);
        }
        return null;
    }

    static Point convert(Point a, double angle) {
        double x = a.x * cos(angle) - a.y * sin(angle);
        double y = a.x * sin(angle) + a.y * cos(angle);
        return new Point(x, y);
    }

    static Point minus(Point a, Point b) {
        return new Point(a.x - b.x, a.y - b.y);
    }

    static Point add(Point a, Point b) {
        return new Point(a.x + b.x, a.y + b.y);
    }

    static double cross(Point a, Point b) {
        return a.x * b.y - a.y * b.x;
    }

    static class Point {

        double x, y;

        Point(double x, double y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public String toString() {
            return "Point: " + x + " " + y;
        }
    }

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() {
            // System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public String next() {

            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}
