#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...);
}
const int MAXN = 1e5 + 5;
const long long INF = 1e9;
struct maxFlow {
  vector<pair<int, int> > e[MAXN];
  vector<long long> cap[MAXN];
  int level[MAXN];
  int nxt[MAXN];
  int s, t;
  int N;
  queue<int> q;
  void init(int n) {
    N = n;
    for (int i = 0; i < N; i++) e[i].clear(), cap[i].clear();
  }
  void addEdge(int x, int y, long long cxy, long long cyx) {
    e[x].push_back({y, cap[y].size()});
    e[y].push_back({x, cap[x].size()});
    cap[x].push_back(cxy);
    cap[y].push_back(cyx);
  }
  bool bfs() {
    while (!q.empty()) q.pop();
    for (int i = 0; i < N; i++) level[i] = -1;
    level[s] = 0;
    q.push(s);
    while (!q.empty()) {
      int p = q.front();
      q.pop();
      if (p == t) return true;
      for (int i = 0; i < (int)e[p].size(); i++) {
        int x = e[p][i].first;
        if (level[x] == -1 && cap[p][i] != 0) {
          level[x] = level[p] + 1;
          q.push(x);
        }
      }
    }
    return false;
  }
  long long augment(int x, long long c) {
    if (x == t) return c;
    for (int &i = nxt[x]; i < (int)e[x].size(); i++) {
      int y = e[x][i].first;
      if (cap[x][i] > 0 && level[y] == level[x] + 1) {
        long long tempFlow = augment(y, min(c, cap[x][i]));
        if (tempFlow > 0) {
          cap[x][i] -= tempFlow;
          cap[y][e[x][i].second] += tempFlow;
          return tempFlow;
        }
      }
    }
    return 0;
  }
  long long solve(int source, int sink) {
    s = source, t = sink;
    long long ans = 0;
    while (bfs()) {
      long long flow = 0;
      for (int i = 0; i < N; i++) nxt[i] = 0;
      while (flow = augment(s, INF)) ans += flow;
    }
    return ans;
  }
};
int nn, mm;
vector<int> dx = {-3, 0, 2, 2, -2, -2, 1, 1, -1, -1, 3, 0};
vector<int> dy = {0, -3, -1, 1, 1, -1, 2, -2, 2, -2, 0, 3};
int getId(int x, int y) { return (x * mm + y); }
bool isValid(int x, int y) { return (x >= 0 && y >= 0 && x < nn && y < mm); }
int main() {
  ios_base ::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long n, m;
  cin >> n >> m;
  nn = n % 300, mm = m % 300;
  maxFlow flowGraph;
  flowGraph.init(nn * mm + 2);
  int source = nn * mm, sink = source + 1;
  for (int i = 0; i < nn; i++) {
    for (int j = 0; j < mm; j++) {
      if ((i + j) & 1) {
        flowGraph.addEdge(source, getId(i, j), 2, 0);
        for (int k = 0; k < 12; k++) {
          int newX = i + dx[k], newY = j + dy[k];
          if (isValid(newX, newY)) {
            flowGraph.addEdge(getId(i, j), getId(newX, newY), INF, 0);
          }
        }
      } else {
        flowGraph.addEdge(getId(i, j), sink, 2, 0);
      }
    }
  }
  cout << n * m - (nn * mm - flowGraph.solve(source, sink));
  return 0;
}

### Prompt

Create a solution in Cpp for the following problem:

Little C loves number «3» very much. He loves all things about it.

Now he is playing a game on a chessboard of size n × m. The cell in the x-th row and in the y-th column is called (x,y). Initially, The chessboard is empty. Each time, he places two chessmen on two different empty cells, the Manhattan distance between which is exactly 3. The Manhattan distance between two cells (x_i,y_i) and (x_j,y_j) is defined as |x_i-x_j|+|y_i-y_j|.

He want to place as many chessmen as possible on the chessboard. Please help him find the maximum number of chessmen he can place.

Input

A single line contains two integers n and m (1 ≤ n,m ≤ 10^9) — the number of rows and the number of columns of the chessboard.

Output

Print one integer — the maximum number of chessmen Little C can place.

Examples

Input

2 2


Output

0

Input

3 3


Output

8

Note

In the first example, the Manhattan distance between any two cells is smaller than 3, so the answer is 0.

In the second example, a possible solution is (1,1)(3,2), (1,2)(3,3), (2,1)(1,3), (3,1)(2,3).

### Response

```cpp
#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...);
}
const int MAXN = 1e5 + 5;
const long long INF = 1e9;
struct maxFlow {
  vector<pair<int, int> > e[MAXN];
  vector<long long> cap[MAXN];
  int level[MAXN];
  int nxt[MAXN];
  int s, t;
  int N;
  queue<int> q;
  void init(int n) {
    N = n;
    for (int i = 0; i < N; i++) e[i].clear(), cap[i].clear();
  }
  void addEdge(int x, int y, long long cxy, long long cyx) {
    e[x].push_back({y, cap[y].size()});
    e[y].push_back({x, cap[x].size()});
    cap[x].push_back(cxy);
    cap[y].push_back(cyx);
  }
  bool bfs() {
    while (!q.empty()) q.pop();
    for (int i = 0; i < N; i++) level[i] = -1;
    level[s] = 0;
    q.push(s);
    while (!q.empty()) {
      int p = q.front();
      q.pop();
      if (p == t) return true;
      for (int i = 0; i < (int)e[p].size(); i++) {
        int x = e[p][i].first;
        if (level[x] == -1 && cap[p][i] != 0) {
          level[x] = level[p] + 1;
          q.push(x);
        }
      }
    }
    return false;
  }
  long long augment(int x, long long c) {
    if (x == t) return c;
    for (int &i = nxt[x]; i < (int)e[x].size(); i++) {
      int y = e[x][i].first;
      if (cap[x][i] > 0 && level[y] == level[x] + 1) {
        long long tempFlow = augment(y, min(c, cap[x][i]));
        if (tempFlow > 0) {
          cap[x][i] -= tempFlow;
          cap[y][e[x][i].second] += tempFlow;
          return tempFlow;
        }
      }
    }
    return 0;
  }
  long long solve(int source, int sink) {
    s = source, t = sink;
    long long ans = 0;
    while (bfs()) {
      long long flow = 0;
      for (int i = 0; i < N; i++) nxt[i] = 0;
      while (flow = augment(s, INF)) ans += flow;
    }
    return ans;
  }
};
int nn, mm;
vector<int> dx = {-3, 0, 2, 2, -2, -2, 1, 1, -1, -1, 3, 0};
vector<int> dy = {0, -3, -1, 1, 1, -1, 2, -2, 2, -2, 0, 3};
int getId(int x, int y) { return (x * mm + y); }
bool isValid(int x, int y) { return (x >= 0 && y >= 0 && x < nn && y < mm); }
int main() {
  ios_base ::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long n, m;
  cin >> n >> m;
  nn = n % 300, mm = m % 300;
  maxFlow flowGraph;
  flowGraph.init(nn * mm + 2);
  int source = nn * mm, sink = source + 1;
  for (int i = 0; i < nn; i++) {
    for (int j = 0; j < mm; j++) {
      if ((i + j) & 1) {
        flowGraph.addEdge(source, getId(i, j), 2, 0);
        for (int k = 0; k < 12; k++) {
          int newX = i + dx[k], newY = j + dy[k];
          if (isValid(newX, newY)) {
            flowGraph.addEdge(getId(i, j), getId(newX, newY), INF, 0);
          }
        }
      } else {
        flowGraph.addEdge(getId(i, j), sink, 2, 0);
      }
    }
  }
  cout << n * m - (nn * mm - flowGraph.solve(source, sink));
  return 0;
}

```