description: On an endless checkered sheet of paper, n cells are chosen and colored in three colors, where n is divisible by 3. It turns out that there are exactly n/3 marked cells of each of three colors! 
  
  Find the largest such k that it's possible to choose k/3 cells of each color, remove all other marked cells, and then select three rectangles with sides parallel to the grid lines so that the following conditions hold:
  
    * No two rectangles can intersect (but they can share a part of the boundary). In other words, the area of intersection of any two of these rectangles must be 0.
    * The i-th rectangle contains all the chosen cells of the i-th color and no chosen cells of other colors, for i = 1, 2, 3. 
  
  Input
  
  The first line of the input contains a single integer n — the number of the marked cells (3 ≤ n ≤ 10^5, n is divisible by 3).
  
  The i-th of the following n lines contains three integers x_i, y_i, c_i (|x_i|,|y_i| ≤ 10^9; 1 ≤ c_i ≤ 3), where (x_i, y_i) are the coordinates of the i-th marked cell and c_i is its color.
  
  It's guaranteed that all cells (x_i, y_i) in the input are distinct, and that there are exactly n/3 cells of each color.
  
  Output
  
  Output a single integer k — the largest number of cells you can leave.
  
  Examples
  
  Input
  
  
  9
  2 3 1
  4 1 2
  2 1 3
  3 4 1
  5 3 2
  4 4 3
  2 4 1
  5 2 2
  3 5 3
  
  
  Output
  
  
  6
  
  
  Input
  
  
  3
  1 1 1
  2 2 2
  3 3 3
  
  
  Output
  
  
  3
  
  Note
  
  In the first sample, it's possible to leave 6 cells with indexes 1, 5, 6, 7, 8, 9.
  
  In the second sample, it's possible to leave 3 cells with indexes 1, 2, 3.
solution: #include <bits/stdc++.h>
  #pragma GCC optimize("Ofast")
  #pragma GCC optimize("unroll-loops")
  using namespace std;
  using ll = long long;
  template <class t, class u>
  bool chmax(t& first, u second) {
    if (first < second) {
      first = second;
      return true;
    } else
      return false;
  }
  template <class t, class u>
  bool chmin(t& first, u second) {
    if (second < first) {
      first = second;
      return true;
    } else
      return false;
  }
  template <class t>
  using vc = vector<t>;
  template <class t>
  using vvc = vc<vc<t>>;
  using pi = pair<int, int>;
  using vi = vc<int>;
  template <class t, class u>
  ostream& operator<<(ostream& os, const pair<t, u>& p) {
    return os << "{" << p.first << "," << p.second << "}";
  }
  template <class t>
  ostream& operator<<(ostream& os, const vc<t>& v) {
    os << "{";
    for (auto e : v) os << e << ",";
    return os << "}";
  }
  using uint = unsigned;
  using ull = unsigned long long;
  template <class t, size_t n>
  ostream& operator<<(ostream& os, const array<t, n>& first) {
    return os << vc<t>(first.begin(), first.end());
  }
  template <int i, class T>
  void print_tuple(ostream&, const T&) {}
  template <int i, class T, class H, class... Args>
  void print_tuple(ostream& os, const T& t) {
    if (i) os << ",";
    os << get<i>(t);
    print_tuple<i + 1, T, Args...>(os, t);
  }
  template <class... Args>
  ostream& operator<<(ostream& os, const tuple<Args...>& t) {
    os << "{";
    print_tuple<0, tuple<Args...>, Args...>(os, t);
    return os << "}";
  }
  template <class t>
  void print(t x, int suc = 1) {
    cout << x;
    if (suc == 1) cout << "\n";
    if (suc == 2) cout << " ";
  }
  ll read() {
    ll i;
    cin >> i;
    return i;
  }
  vi readvi(int n, int off = 0) {
    vi v(n);
    for (int i = int(0); i < int(n); i++) v[i] = read() + off;
    return v;
  }
  pi readpi(int off = 0) {
    int first, second;
    cin >> first >> second;
    return pi(first + off, second + off);
  }
  template <class t, class u>
  void print(const pair<t, u>& p, int suc = 1) {
    print(p.first, 2);
    print(p.second, suc);
  }
  template <class T>
  void print(const vector<T>& v, int suc = 1) {
    for (int i = int(0); i < int(v.size()); i++)
      print(v[i], i == int(v.size()) - 1 ? suc : 2);
  }
  template <class T>
  void print_offset(const vector<T>& v, ll off, int suc = 1) {
    for (int i = int(0); i < int(v.size()); i++)
      print(v[i] + off, i == int(v.size()) - 1 ? suc : 2);
  }
  template <class T, size_t N>
  void print(const array<T, N>& v, int suc = 1) {
    for (int i = int(0); i < int(N); i++) print(v[i], i == int(N) - 1 ? suc : 2);
  }
  string readString() {
    string s;
    cin >> s;
    return s;
  }
  template <class T>
  T sq(const T& t) {
    return t * t;
  }
  void yes(bool ex = true) {
    cout << "Yes"
         << "\n";
    if (ex) exit(0);
  }
  void no(bool ex = true) {
    cout << "No"
         << "\n";
    if (ex) exit(0);
  }
  void possible(bool ex = true) {
    cout << "Possible"
         << "\n";
    if (ex) exit(0);
  }
  void impossible(bool ex = true) {
    cout << "Impossible"
         << "\n";
    if (ex) exit(0);
  }
  constexpr ll ten(int n) { return n == 0 ? 1 : ten(n - 1) * 10; }
  const ll infLL = LLONG_MAX / 3;
  const int inf = INT_MAX / 2 - 100;
  int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
  int topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
  int botbit(signed first) { return first == 0 ? 32 : __builtin_ctz(first); }
  int botbit(ll first) { return first == 0 ? 64 : __builtin_ctzll(first); }
  int popcount(signed t) { return __builtin_popcount(t); }
  int popcount(ll t) { return __builtin_popcountll(t); }
  bool ispow2(int i) { return i && (i & -i) == i; }
  ll mask(int i) { return (ll(1) << i) - 1; }
  bool inc(int first, int second, int c) {
    return first <= second && second <= c;
  }
  template <class t>
  void mkuni(vc<t>& v) {
    sort(v.begin(), v.end());
    v.erase(unique(v.begin(), v.end()), v.end());
  }
  ll rand_int(ll l, ll r) {
    static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
    return uniform_int_distribution<ll>(l, r)(gen);
  }
  template <class t>
  void myshuffle(vc<t>& first) {
    for (int i = int(0); i < int(int(first.size())); i++)
      swap(first[i], first[rand_int(0, i)]);
  }
  template <class t>
  int lwb(const vc<t>& v, const t& first) {
    return lower_bound(v.begin(), v.end(), first) - v.begin();
  }
  vvc<int> readGraph(int n, int m) {
    vvc<int> g(n);
    for (int i = int(0); i < int(m); i++) {
      int first, second;
      cin >> first >> second;
      first--;
      second--;
      g[first].push_back(second);
      g[second].push_back(first);
    }
    return g;
  }
  vvc<int> readTree(int n) { return readGraph(n, n - 1); }
  struct P {
    int x, y, c;
    void readinit() {
      cin >> x >> y >> c;
      c--;
    }
    void rot() { tie(x, y) = pi(-y, x); }
  };
  void slv() {
    int n;
    cin >> n;
    vc<P> ps(n);
    for (int i = int(0); i < int(n); i++) ps[i].readinit();
    int lw = 0, up = n / 3 + 1;
    vi first, second, c;
    while (up - lw > 1) {
      const int mid = (lw + up) / 2;
      bool ok = false;
      for (int dir = int(0); dir < int(4); dir++)
        if (!ok) {
          for (int ini = int(0); ini < int(3); ini++)
            if (!ok) {
              first.clear();
              for (int i = int(0); i < int(n); i++)
                if (ps[i].c == ini) first.push_back(ps[i].x);
              nth_element(first.begin(), first.begin() + (mid - 1), first.end());
              int lf = first[mid - 1];
              for (int _ = int(0); _ < int(2); _++) {
                second.clear();
                c.clear();
                for (int i = int(0); i < int(n); i++)
                  if (lf < ps[i].x) {
                    if (ps[i].c == (ini + 1) % 3) {
                      second.push_back(_ == 0 ? ps[i].x : ps[i].y);
                    } else if (ps[i].c == (ini + 2) % 3) {
                      c.push_back(_ == 0 ? ps[i].x : ps[i].y);
                    }
                  }
                if (int(second.size()) >= mid && int(c.size()) >= mid) {
                  for (int $ = int(0); $ < int(2); $++) {
                    nth_element(second.begin(), second.begin() + (mid - 1),
                                second.end());
                    nth_element(c.begin(), c.end() - mid, c.end());
                    if (second[mid - 1] < c[int(c.size()) - mid]) {
                      ok = true;
                    }
                    swap(second, c);
                  }
                }
              }
            }
          for (int i = int(0); i < int(n); i++) {
            ps[i].rot();
          }
        }
      if (ok)
        lw = mid;
      else
        up = mid;
    }
    print(lw * 3);
  }
  signed main() {
    cin.tie(0);
    ios::sync_with_stdio(0);
    cout << fixed << setprecision(20);
    slv();
  }
  