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.
#include <bits/stdc++.h>
using namespace std;
void __print(int x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(long long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\'' << x << '\''; }
void __print(const char *x) { cerr << '\"' << x << '\"'; }
void __print(const string &x) { cerr << '\"' << x << '\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }
template <typename T, typename V>
void __print(const pair<T, V> &x) {
  cerr << '{';
  __print(x.first);
  cerr << ',';
  __print(x.second);
  cerr << '}';
}
template <typename T>
void __print(const T &x) {
  int f = 0;
  cerr << '{';
  for (auto &i : x) cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void _print() { cerr << "]\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v)) cerr << ", ";
  _print(v...);
}
struct custom_hash {
  static uint64_t splitmix64(uint64_t x) {
    x += 0x9e3779b97f4a7c15;
    x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
    x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
    return x ^ (x >> 31);
  }
  size_t operator()(uint64_t x) const {
    static const uint64_t FIXED_RANDOM =
        chrono::steady_clock::now().time_since_epoch().count();
    return splitmix64(x + FIXED_RANDOM);
  }
};
int power(long long x, long long n, const long long P) {
  if (x == 0) return 0;
  if (n == 0 || x == 1) return 1LL;
  x %= P;
  int res = 1;
  while (n > 0) {
    if (n & 1) res = (long long int)res * x % P;
    x = (long long int)x * x % P;
    n /= 2;
  }
  return res;
}
long long int power(long long int x, long long int n) {
  if (x == 0)
    return 0;
  else if (n == 0 || x == 1)
    return 1;
  long long res = 1;
  while (n > 0) {
    if (n & 1) res *= x;
    x *= x;
    n /= 2;
  }
  return res;
}
int inv(long long x) { return power(x, 1000000007 - 2, 1000000007); }
long long int gcd(const long long int a, const long long int b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long int lcm(const long long int a, const long long int b) {
  return (a * b) / gcd(a, b);
}
pair<int, int> dx[4] = {make_pair(-1, 0), make_pair(1, 0), make_pair(0, -1),
                        make_pair(0, 1)};
bool valid(const int &last, const int &cur, const int &next, int const &n) {
  for (int i = 0; i < n; i++) {
    if (!((1 << i) & cur)) {
      bool f = 0;
      if (i && ((1 << (i - 1)) & cur))
        f = 1;
      else if (i + 1 < n && ((1 << (i + 1)) & cur))
        f = 1;
      else if ((1 << i) & last)
        f = 1;
      else if ((1 << i) & next)
        f = 1;
      if (!f) return false;
    }
  }
  return true;
}
void __sol() {
  int n, m;
  cin >> n >> m;
  if (n > 6) swap(n, m);
  int dp[m + 2][1 << n][1 << n];
  for (int i = 0; i < m + 2; i++)
    for (int j = 0; j < 1 << n; j++)
      for (int k = 0; k < 1 << n; k++) dp[i][j][k] = INT_MAX / 1000;
  for (int i = 1; i <= m; i++) {
    for (int pm = 0; pm < 1 << n; pm++) {
      for (int nm = 0; nm < 1 << n; nm++) {
        for (int lm = 0; lm < 1 << n; lm++) {
          if (i == 1 && valid(0, pm, nm, n))
            dp[i][pm][nm] = min(dp[i][pm][nm], __builtin_popcount(pm));
          else if (i == m && valid(lm, pm, 0, n))
            dp[i][pm][0] =
                min(dp[i][pm][0], __builtin_popcount(pm) + dp[i - 1][lm][pm]);
          else if (i != 1 && i != m && valid(lm, pm, nm, n))
            dp[i][pm][nm] =
                min(dp[i][pm][nm], __builtin_popcount(pm) + dp[i - 1][lm][pm]);
        }
      }
    }
  }
  int ans = INT_MAX / 1000;
  for (int i = 0; i < 1 << n; i++) ans = min(ans, dp[m][i][0]);
  cout << n * m - ans;
  return;
}
int main() {
  clock_t time_req = clock();
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long int tc = 1;
  while (tc--) __sol();
  time_req = clock() - time_req;
  return 0;
}
