Problem p02581 (C++) — buggy submission, verdict: Runtime Error

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <climits>
#include <cmath>
#include <complex>
#include <cstring>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <vector>

using namespace std;
#define ll long long
#define ull unsigned long long
#define rep(i, m, n) for (ll(i) = (ll)(m); i < (ll)(n); i++)
#define REP(i, n) rep(i, 0, n)
#define all(hoge) (hoge).begin(), (hoge).end()
typedef pair<ll, ll> P;
constexpr long double m_pi = 3.1415926535897932L;
constexpr ll MOD = 1000000007;
constexpr ll INF = 1LL << 61;
constexpr long double EPS = 1e-10;
template <typename T> using vector2 = vector<vector<T>>;
template <typename T> using vector3 = vector<vector2<T>>;
typedef vector<ll> Array;
typedef vector<Array> Matrix;
string operator*(const string &s, int k) {
  if (k == 0)
    return "";
  string p = (s + s) * (k / 2);
  if (k % 2 == 1)
    p += s;
  return p;
}

template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}

struct Edge { // グラフ
  int to, rev;
  ll cap;
  Edge(int _to, ll _cap, int _rev) {
    to = _to;
    cap = _cap;
    rev = _rev;
  }
};
typedef vector<Edge> Edges;
typedef vector<Edges> Graph;
void add_edge(Graph &G, int from, int to, ll cap, bool revFlag,
              ll revCap) { // 最大フロー求める Ford-fulkerson
  G[from].push_back(Edge(to, cap, (ll)G[to].size() + (from == to)));
  if (revFlag)
    G[to].push_back(Edge(
        from, revCap, (ll)G[from].size() - 1)); // 最小カットの場合逆辺は0にする
}

ll max_flow_dfs(Graph &G, ll v, ll t, ll f, vector<bool> &used) {
  if (v == t)
    return f;
  used[v] = true;
  for (int i = 0; i < G[v].size(); ++i) {
    Edge &e = G[v][i];
    if (!used[e.to] && e.cap > 0) {
      ll d = max_flow_dfs(G, e.to, t, min(f, e.cap), used);
      if (d > 0) {
        e.cap -= d;
        G[e.to][e.rev].cap += d;
        return d;
      }
    }
  }
  return 0;
}
// 二分グラフの最大マッチングを求めたりも出来る　また二部グラフの最大独立集合は頂点数-最大マッチングのサイズ
ll max_flow(Graph &G, ll s, ll t) // O(V(V+E))
{
  ll flow = 0;
  for (;;) {
    vector<bool> used(G.size());
    REP(i, used.size()) used[i] = false;
    ll f = max_flow_dfs(G, s, t, INF, used);
    if (f == 0) {
      return flow;
    }
    flow += f;
  }
}

void BellmanFord(Graph &G, ll s, Array &d, Array &negative) { // O(|E||V|)
  d.resize(G.size());
  negative.resize(G.size());
  REP(i, d.size()) d[i] = INF;
  REP(i, d.size()) negative[i] = false;
  d[s] = 0;
  REP(k, G.size() - 1) {
    REP(i, G.size()) {
      REP(j, G[i].size()) {
        if (d[i] != INF && d[G[i][j].to] > d[i] + G[i][j].cap) {
          d[G[i][j].to] = d[i] + G[i][j].cap;
        }
      }
    }
  }
  REP(k, G.size() - 1) {
    REP(i, G.size()) {
      REP(j, G[i].size()) {
        if (d[i] != INF && d[G[i][j].to] > d[i] + G[i][j].cap) {
          d[G[i][j].to] = d[i] + G[i][j].cap;
          negative[G[i][j].to] = true;
        }
        if (negative[i] == true)
          negative[G[i][j].to] = true;
      }
    }
  }
}
void Dijkstra(Graph &G, ll s, Array &d) { // O(|E|log|V|)
  d.resize(G.size());
  REP(i, d.size()) d[i] = INF;
  d[s] = 0;
  priority_queue<P, vector<P>, greater<P>> q;
  q.push(make_pair(0, s));
  while (!q.empty()) {
    P a = q.top();
    q.pop();
    if (d[a.second] < a.first)
      continue;
    REP(i, G[a.second].size()) {
      Edge e = G[a.second][i];
      if (d[e.to] > d[a.second] + e.cap) {
        d[e.to] = d[a.second] + e.cap;
        q.push(make_pair(d[e.to], e.to));
      }
    }
  }
}
void WarshallFloyd(Graph &G, Matrix &d) { // O(V^3)
  d.resize(G.size());
  REP(i, d.size()) d[i].resize(G.size());
  REP(i, d.size()) {
    REP(j, d[i].size()) { d[i][j] = ((i != j) ? INF : 0); }
  }
  REP(i, G.size()) {
    REP(j, G[i].size()) { chmin(d[i][G[i][j].to], G[i][j].cap); }
  }
  REP(i, G.size()) {
    REP(j, G.size()) {
      REP(k, G.size()) {
        if (d[j][i] != INF && d[i][k] != INF)
          chmin(d[j][k], d[j][i] + d[i][k]);
      }
    }
  }
}
bool tsort(Graph &graph, vector<int> &order) { // トポロジカルソートO(E+V)
  int n = graph.size(), k = 0;
  vector<int> in(n);
  for (auto &es : graph)
    for (auto &e : es)
      in[e.to]++;
  priority_queue<int, vector<int>, greater<int>> que;
  REP(i, n)
  if (in[i] == 0)
    que.push(i);
  while (que.size()) {
    int v = que.top();
    que.pop();
    order.push_back(v);
    for (auto &e : graph[v])
      if (--in[e.to] == 0)
        que.push(e.to);
  }
  if (order.size() != n)
    return false;
  else
    return true;
}
class Lca {
public:
  const int n = 0;
  const int log2_n = 0;
  std::vector<std::vector<int>> parent;
  std::vector<int> depth;

  Lca() {}

  Lca(const Graph &g, int root)
      : n(g.size()), log2_n(log2(n) + 1), parent(log2_n, std::vector<int>(n)),
        depth(n) {
    dfs(g, root, -1, 0);
    for (int k = 0; k + 1 < log2_n; k++) {
      for (int v = 0; v < (int)g.size(); v++) {
        if (parent[k][v] < 0)
          parent[k + 1][v] = -1;
        else
          parent[k + 1][v] = parent[k][parent[k][v]];
      }
    }
  }

  void dfs(const Graph &g, int v, int p, int d) {
    parent[0][v] = p;
    depth[v] = d;
    for (auto &e : g[v]) {
      if (e.to != p)
        dfs(g, e.to, v, d + 1);
    }
  }

  int get(int u, int v) {
    if (depth[u] > depth[v])
      std::swap(u, v);
    for (int k = 0; k < log2_n; k++) {
      if ((depth[v] - depth[u]) >> k & 1) {
        v = parent[k][v];
      }
    }
    if (u == v)
      return u;
    for (int k = log2_n - 1; k >= 0; k--) {
      if (parent[k][u] != parent[k][v]) {
        u = parent[k][u];
        v = parent[k][v];
      }
    }
    return parent[0][u];
  }
};

class UnionFind {
  vector<int> data;
  int num;

public:
  UnionFind(int size) : data(size, -1), num(size) {}
  bool unite(int x, int y) { // xとyの集合を統合する
    x = root(x);
    y = root(y);
    if (x != y) {
      if (data[y] < data[x])
        swap(x, y);
      data[x] += data[y];
      data[y] = x;
    }
    num -= (x != y);
    return x != y;
  }
  bool findSet(int x, int y) { // xとyが同じ集合か返す
    return root(x) == root(y);
  }
  int root(int x) { // xのルートを返す
    return data[x] < 0 ? x : data[x] = root(data[x]);
  }
  int size(int x) { // xの集合のサイズを返す
    return -data[root(x)];
  }
  int numSet() { // 集合の数を返す
    return num;
  }
};

template <typename T, typename F> class SegmentTree {
private:
  T identity;
  F merge;
  ll n;
  vector<T> dat;

public:
  SegmentTree(F f, T id, vector<T> v) : merge(f), identity(id) {
    int _n = v.size();
    n = 1;
    while (n < _n)
      n *= 2;
    dat.resize(2 * n - 1, identity);
    REP(i, _n) dat[n + i - 1] = v[i];
    for (int i = n - 2; i >= 0; i--)
      dat[i] = merge(dat[i * 2 + 1], dat[i * 2 + 2]);
  }
  SegmentTree(F f, T id, int _n) : merge(f), identity(id) {
    n = 1;
    while (n < _n)
      n *= 2;
    dat.resize(2 * n - 1, identity);
  }
  void set_val(int i, T x) {
    i += n - 1;
    dat[i] = x;
    while (i > 0) {
      i = (i - 1) / 2;
      dat[i] = merge(dat[i * 2 + 1], dat[i * 2 + 2]);
    }
  }
  T query(int l, int r) {
    T left = identity, right = identity;
    l += n - 1;
    r += n - 1;
    while (l < r) {
      if ((l & 1) == 0)
        left = merge(left, dat[l]);
      if ((r & 1) == 0)
        right = merge(dat[r - 1], right);
      l = l / 2;
      r = (r - 1) / 2;
    }
    return merge(left, right);
  }
};

template <typename T> class FenwickTree {
  vector<T> data;
  int n;
  int p;

public:
  FenwickTree(int n) : n(n) {
    data.resize(n + 1LL, 0);
    p = 1;
    while (p < data.size())
      p *= 2;
  }
  T sum(int k) {
    T ret = 0;
    for (; k > 0; k -= k & -k)
      ret += data[k];
    return (ret);
  }

  T sum(int a, int b) { return sum(b) - sum(a); } //[a,b)

  void add(int k, T x) {
    for (++k; k <= n; k += k & -k)
      data[k] += x;
  }

  int lower_bound(ll w) {
    if (w <= 0)
      return -1;
    int x = 0;
    for (int k = p / 2; k > 0; k /= 2) {
      if (x + k <= n && data[x + k] < w)
        w -= data[x + k], x += k;
    }
    return x;
  }
};

// 約数求める //約数
void divisor(ll n, vector<ll> &ret) {
  for (ll i = 1; i * i <= n; i++) {
    if (n % i == 0) {
      ret.push_back(i);
      if (i * i != n)
        ret.push_back(n / i);
    }
  }
  sort(ret.begin(), ret.end());
}

void prime_factorization(ll n, vector<P> &ret) {
  for (ll i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      ret.push_back({i, 0});
      while (n % i == 0) {
        n /= i;
        ret[ret.size() - 1].second++;
      }
    }
  }
  if (n != 1)
    ret.push_back({n, 1});
}

inline ll mod_pow(ll x, ll n, ll mod) {
  ll res = 1;
  while (n > 0) {
    if (n & 1)
      res = res * x % mod;
    x = x * x % mod;
    n >>= 1;
  }
  return res;
}

inline ll mod_inv(ll x, ll mod) { return mod_pow(x, mod - 2, mod); }

class Combination {
public:
  Array fact;
  Array fact_inv;
  ll mod;
  // if n >= mod use lucas
  ll nCr(ll n, ll r) {
    if (n < r)
      return 0;
    if (n < mod)
      return ((fact[n] * fact_inv[r] % mod) * fact_inv[n - r]) % mod;

    ll ret = 1;
    while (n || r) {
      ll _n = n % mod, _r = r % mod;
      n /= mod;
      r /= mod;
      (ret *= nCr(_n, _r)) %= mod;
    }
    return ret;
  }
  ll nPr(ll n, ll r) { return (fact[n] * fact_inv[n - r]) % mod; }
  ll nHr(ll n, ll r) { return nCr(r + n - 1, r); }
  Combination(ll _n, ll _mod) {
    mod = _mod;
    ll n = min(_n + 1, mod);
    fact.resize(n);
    fact[0] = 1;
    REP(i, n - 1) { fact[i + 1] = (fact[i] * (i + 1LL)) % mod; }
    fact_inv.resize(n);
    fact_inv[n - 1] = mod_inv(fact[n - 1], mod);
    for (int i = n - 1; i > 0; i--) {
      fact_inv[i - 1] = fact_inv[i] * i % mod;
    }
  }
};

ll popcount(ll x) {
  x = (x & 0x5555555555555555) + (x >> 1 & 0x5555555555555555);
  x = (x & 0x3333333333333333) + (x >> 2 & 0x3333333333333333);
  x = (x & 0x0F0F0F0F0F0F0F0F) + (x >> 4 & 0x0F0F0F0F0F0F0F0F);
  x = (x & 0x00FF00FF00FF00FF) + (x >> 8 & 0x00FF00FF00FF00FF);
  x = (x & 0x0000FFFF0000FFFF) + (x >> 16 & 0x0000FFFF0000FFFF);
  x = (x & 0x00000000FFFFFFFF) + (x >> 32 & 0x00000000FFFFFFFF);

  return x;
}

ll dp[2020][2020];

int main() {
  ios::sync_with_stdio(false);
  std::cin.tie(0);
  std::cout.tie(0);

  ll n;
  cin >> n;
  Array a(3 * n);
  for (auto &e : a)
    cin >> e, e--;
  Array p(n, -INF);
  REP(i, 2020) REP(j, 2020) dp[i][j] = -INF;
  dp[a[0]][a[1]] = dp[a[1]][a[0]] = 0;
  p[a[0]] = p[a[1]] = 0;
  ll ans = 0;
  ll tmp = 0;
  REP(i, n - 1) {
    ll x = a[3 * i + 2], y = a[3 * i + 3], z = a[3 * i + 4];
    if (x == y && x == z) {
      tmp++;
      continue;
    }
    vector<tuple<ll, ll, ll>> update;
    ll mx = *max_element(all(p));
    if (x == y)
      REP(j, n) update.push_back({j, z, dp[x][j] + 1});
    if (y == z)
      REP(j, n) update.push_back({j, x, dp[y][j] + 1});
    if (x == z)
      REP(j, n) update.push_back({j, y, dp[z][j] + 1});
    update.push_back({x, y, dp[z][z] + 1});
    update.push_back({y, z, dp[x][x] + 1});
    update.push_back({x, z, dp[y][y] + 1});
    update.push_back({x, y, mx});
    update.push_back({y, z, mx});
    update.push_back({x, z, mx});
    REP(j, n) update.push_back({j, x, p[j]});
    REP(j, n) update.push_back({j, y, p[j]});
    REP(j, n) update.push_back({j, z, p[j]});
    for (auto [u, v, c] : update) {
      chmax(dp[u][v], c);
      chmax(dp[v][u], c);
      chmax(p[u], c);
      chmax(p[v], c);
    }
  }
  REP(i, n) REP(j, n) {
    chmax(ans, dp[i][j]);
    if (i == j && i == a.back())
      chmax(ans, dp[i][j] + 1);
  }

  cout << ans + tmp << "\\n";

  return 0;
}

Error: 0

Fixed submission:

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <climits>
#include <cmath>
#include <complex>
#include <cstring>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <vector>

using namespace std;
#define ll long long
#define ull unsigned long long
#define rep(i, m, n) for (ll(i) = (ll)(m); i < (ll)(n); i++)
#define REP(i, n) rep(i, 0, n)
#define all(hoge) (hoge).begin(), (hoge).end()
typedef pair<ll, ll> P;
constexpr long double m_pi = 3.1415926535897932L;
constexpr ll MOD = 1000000007;
constexpr ll INF = 1LL << 61;
constexpr long double EPS = 1e-10;
template <typename T> using vector2 = vector<vector<T>>;
template <typename T> using vector3 = vector<vector2<T>>;
typedef vector<ll> Array;
typedef vector<Array> Matrix;
string operator*(const string &s, int k) {
  if (k == 0)
    return "";
  string p = (s + s) * (k / 2);
  if (k % 2 == 1)
    p += s;
  return p;
}

template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}

struct Edge { // グラフ
  int to, rev;
  ll cap;
  Edge(int _to, ll _cap, int _rev) {
    to = _to;
    cap = _cap;
    rev = _rev;
  }
};
typedef vector<Edge> Edges;
typedef vector<Edges> Graph;
void add_edge(Graph &G, int from, int to, ll cap, bool revFlag,
              ll revCap) { // 最大フロー求める Ford-fulkerson
  G[from].push_back(Edge(to, cap, (ll)G[to].size() + (from == to)));
  if (revFlag)
    G[to].push_back(Edge(
        from, revCap, (ll)G[from].size() - 1)); // 最小カットの場合逆辺は0にする
}

ll max_flow_dfs(Graph &G, ll v, ll t, ll f, vector<bool> &used) {
  if (v == t)
    return f;
  used[v] = true;
  for (int i = 0; i < G[v].size(); ++i) {
    Edge &e = G[v][i];
    if (!used[e.to] && e.cap > 0) {
      ll d = max_flow_dfs(G, e.to, t, min(f, e.cap), used);
      if (d > 0) {
        e.cap -= d;
        G[e.to][e.rev].cap += d;
        return d;
      }
    }
  }
  return 0;
}
// 二分グラフの最大マッチングを求めたりも出来る　また二部グラフの最大独立集合は頂点数-最大マッチングのサイズ
ll max_flow(Graph &G, ll s, ll t) // O(V(V+E))
{
  ll flow = 0;
  for (;;) {
    vector<bool> used(G.size());
    REP(i, used.size()) used[i] = false;
    ll f = max_flow_dfs(G, s, t, INF, used);
    if (f == 0) {
      return flow;
    }
    flow += f;
  }
}

void BellmanFord(Graph &G, ll s, Array &d, Array &negative) { // O(|E||V|)
  d.resize(G.size());
  negative.resize(G.size());
  REP(i, d.size()) d[i] = INF;
  REP(i, d.size()) negative[i] = false;
  d[s] = 0;
  REP(k, G.size() - 1) {
    REP(i, G.size()) {
      REP(j, G[i].size()) {
        if (d[i] != INF && d[G[i][j].to] > d[i] + G[i][j].cap) {
          d[G[i][j].to] = d[i] + G[i][j].cap;
        }
      }
    }
  }
  REP(k, G.size() - 1) {
    REP(i, G.size()) {
      REP(j, G[i].size()) {
        if (d[i] != INF && d[G[i][j].to] > d[i] + G[i][j].cap) {
          d[G[i][j].to] = d[i] + G[i][j].cap;
          negative[G[i][j].to] = true;
        }
        if (negative[i] == true)
          negative[G[i][j].to] = true;
      }
    }
  }
}
void Dijkstra(Graph &G, ll s, Array &d) { // O(|E|log|V|)
  d.resize(G.size());
  REP(i, d.size()) d[i] = INF;
  d[s] = 0;
  priority_queue<P, vector<P>, greater<P>> q;
  q.push(make_pair(0, s));
  while (!q.empty()) {
    P a = q.top();
    q.pop();
    if (d[a.second] < a.first)
      continue;
    REP(i, G[a.second].size()) {
      Edge e = G[a.second][i];
      if (d[e.to] > d[a.second] + e.cap) {
        d[e.to] = d[a.second] + e.cap;
        q.push(make_pair(d[e.to], e.to));
      }
    }
  }
}
void WarshallFloyd(Graph &G, Matrix &d) { // O(V^3)
  d.resize(G.size());
  REP(i, d.size()) d[i].resize(G.size());
  REP(i, d.size()) {
    REP(j, d[i].size()) { d[i][j] = ((i != j) ? INF : 0); }
  }
  REP(i, G.size()) {
    REP(j, G[i].size()) { chmin(d[i][G[i][j].to], G[i][j].cap); }
  }
  REP(i, G.size()) {
    REP(j, G.size()) {
      REP(k, G.size()) {
        if (d[j][i] != INF && d[i][k] != INF)
          chmin(d[j][k], d[j][i] + d[i][k]);
      }
    }
  }
}
bool tsort(Graph &graph, vector<int> &order) { // トポロジカルソートO(E+V)
  int n = graph.size(), k = 0;
  vector<int> in(n);
  for (auto &es : graph)
    for (auto &e : es)
      in[e.to]++;
  priority_queue<int, vector<int>, greater<int>> que;
  REP(i, n)
  if (in[i] == 0)
    que.push(i);
  while (que.size()) {
    int v = que.top();
    que.pop();
    order.push_back(v);
    for (auto &e : graph[v])
      if (--in[e.to] == 0)
        que.push(e.to);
  }
  if (order.size() != n)
    return false;
  else
    return true;
}
class Lca {
public:
  const int n = 0;
  const int log2_n = 0;
  std::vector<std::vector<int>> parent;
  std::vector<int> depth;

  Lca() {}

  Lca(const Graph &g, int root)
      : n(g.size()), log2_n(log2(n) + 1), parent(log2_n, std::vector<int>(n)),
        depth(n) {
    dfs(g, root, -1, 0);
    for (int k = 0; k + 1 < log2_n; k++) {
      for (int v = 0; v < (int)g.size(); v++) {
        if (parent[k][v] < 0)
          parent[k + 1][v] = -1;
        else
          parent[k + 1][v] = parent[k][parent[k][v]];
      }
    }
  }

  void dfs(const Graph &g, int v, int p, int d) {
    parent[0][v] = p;
    depth[v] = d;
    for (auto &e : g[v]) {
      if (e.to != p)
        dfs(g, e.to, v, d + 1);
    }
  }

  int get(int u, int v) {
    if (depth[u] > depth[v])
      std::swap(u, v);
    for (int k = 0; k < log2_n; k++) {
      if ((depth[v] - depth[u]) >> k & 1) {
        v = parent[k][v];
      }
    }
    if (u == v)
      return u;
    for (int k = log2_n - 1; k >= 0; k--) {
      if (parent[k][u] != parent[k][v]) {
        u = parent[k][u];
        v = parent[k][v];
      }
    }
    return parent[0][u];
  }
};

class UnionFind {
  vector<int> data;
  int num;

public:
  UnionFind(int size) : data(size, -1), num(size) {}
  bool unite(int x, int y) { // xとyの集合を統合する
    x = root(x);
    y = root(y);
    if (x != y) {
      if (data[y] < data[x])
        swap(x, y);
      data[x] += data[y];
      data[y] = x;
    }
    num -= (x != y);
    return x != y;
  }
  bool findSet(int x, int y) { // xとyが同じ集合か返す
    return root(x) == root(y);
  }
  int root(int x) { // xのルートを返す
    return data[x] < 0 ? x : data[x] = root(data[x]);
  }
  int size(int x) { // xの集合のサイズを返す
    return -data[root(x)];
  }
  int numSet() { // 集合の数を返す
    return num;
  }
};

template <typename T, typename F> class SegmentTree {
private:
  T identity;
  F merge;
  ll n;
  vector<T> dat;

public:
  SegmentTree(F f, T id, vector<T> v) : merge(f), identity(id) {
    int _n = v.size();
    n = 1;
    while (n < _n)
      n *= 2;
    dat.resize(2 * n - 1, identity);
    REP(i, _n) dat[n + i - 1] = v[i];
    for (int i = n - 2; i >= 0; i--)
      dat[i] = merge(dat[i * 2 + 1], dat[i * 2 + 2]);
  }
  SegmentTree(F f, T id, int _n) : merge(f), identity(id) {
    n = 1;
    while (n < _n)
      n *= 2;
    dat.resize(2 * n - 1, identity);
  }
  void set_val(int i, T x) {
    i += n - 1;
    dat[i] = x;
    while (i > 0) {
      i = (i - 1) / 2;
      dat[i] = merge(dat[i * 2 + 1], dat[i * 2 + 2]);
    }
  }
  T query(int l, int r) {
    T left = identity, right = identity;
    l += n - 1;
    r += n - 1;
    while (l < r) {
      if ((l & 1) == 0)
        left = merge(left, dat[l]);
      if ((r & 1) == 0)
        right = merge(dat[r - 1], right);
      l = l / 2;
      r = (r - 1) / 2;
    }
    return merge(left, right);
  }
};

template <typename T> class FenwickTree {
  vector<T> data;
  int n;
  int p;

public:
  FenwickTree(int n) : n(n) {
    data.resize(n + 1LL, 0);
    p = 1;
    while (p < data.size())
      p *= 2;
  }
  T sum(int k) {
    T ret = 0;
    for (; k > 0; k -= k & -k)
      ret += data[k];
    return (ret);
  }

  T sum(int a, int b) { return sum(b) - sum(a); } //[a,b)

  void add(int k, T x) {
    for (++k; k <= n; k += k & -k)
      data[k] += x;
  }

  int lower_bound(ll w) {
    if (w <= 0)
      return -1;
    int x = 0;
    for (int k = p / 2; k > 0; k /= 2) {
      if (x + k <= n && data[x + k] < w)
        w -= data[x + k], x += k;
    }
    return x;
  }
};

// 約数求める //約数
void divisor(ll n, vector<ll> &ret) {
  for (ll i = 1; i * i <= n; i++) {
    if (n % i == 0) {
      ret.push_back(i);
      if (i * i != n)
        ret.push_back(n / i);
    }
  }
  sort(ret.begin(), ret.end());
}

void prime_factorization(ll n, vector<P> &ret) {
  for (ll i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      ret.push_back({i, 0});
      while (n % i == 0) {
        n /= i;
        ret[ret.size() - 1].second++;
      }
    }
  }
  if (n != 1)
    ret.push_back({n, 1});
}

inline ll mod_pow(ll x, ll n, ll mod) {
  ll res = 1;
  while (n > 0) {
    if (n & 1)
      res = res * x % mod;
    x = x * x % mod;
    n >>= 1;
  }
  return res;
}

inline ll mod_inv(ll x, ll mod) { return mod_pow(x, mod - 2, mod); }

class Combination {
public:
  Array fact;
  Array fact_inv;
  ll mod;
  // if n >= mod use lucas
  ll nCr(ll n, ll r) {
    if (n < r)
      return 0;
    if (n < mod)
      return ((fact[n] * fact_inv[r] % mod) * fact_inv[n - r]) % mod;

    ll ret = 1;
    while (n || r) {
      ll _n = n % mod, _r = r % mod;
      n /= mod;
      r /= mod;
      (ret *= nCr(_n, _r)) %= mod;
    }
    return ret;
  }
  ll nPr(ll n, ll r) { return (fact[n] * fact_inv[n - r]) % mod; }
  ll nHr(ll n, ll r) { return nCr(r + n - 1, r); }
  Combination(ll _n, ll _mod) {
    mod = _mod;
    ll n = min(_n + 1, mod);
    fact.resize(n);
    fact[0] = 1;
    REP(i, n - 1) { fact[i + 1] = (fact[i] * (i + 1LL)) % mod; }
    fact_inv.resize(n);
    fact_inv[n - 1] = mod_inv(fact[n - 1], mod);
    for (int i = n - 1; i > 0; i--) {
      fact_inv[i - 1] = fact_inv[i] * i % mod;
    }
  }
};

ll popcount(ll x) {
  x = (x & 0x5555555555555555) + (x >> 1 & 0x5555555555555555);
  x = (x & 0x3333333333333333) + (x >> 2 & 0x3333333333333333);
  x = (x & 0x0F0F0F0F0F0F0F0F) + (x >> 4 & 0x0F0F0F0F0F0F0F0F);
  x = (x & 0x00FF00FF00FF00FF) + (x >> 8 & 0x00FF00FF00FF00FF);
  x = (x & 0x0000FFFF0000FFFF) + (x >> 16 & 0x0000FFFF0000FFFF);
  x = (x & 0x00000000FFFFFFFF) + (x >> 32 & 0x00000000FFFFFFFF);

  return x;
}

int main() {
  ios::sync_with_stdio(false);
  std::cin.tie(0);
  std::cout.tie(0);

  ll n;
  cin >> n;
  Array a(3 * n);
  for (auto &e : a)
    cin >> e;
  map<Array, ll> mp;
  mp[{a[0], a[1]}] = 0;
  ll mx = 0;
  REP(i, n - 1) {
    map<Array, ll> nxt;
    ll mx_t = mx;
    assert(mp.size() <= 2020);
    for (auto [p, c] : mp) {
      //	if (c <= mx_t - 2)continue;
      Array t = {a[3 * i + 2], a[3 * i + 3], a[3 * i + 4], p[0], p[1]};

      REP(j, 32) {
        if (popcount(j) != 3)
          continue;
        map<ll, ll> tmp;
        Array pp;
        REP(k, 5) {
          if (j & (1LL << k))
            tmp[t[k]]++;
          else
            pp.push_back(t[k]);
        }
        if (pp[0] > pp[1])
          swap(pp[0], pp[1]);
        auto push = [&](ll c) {
          if (nxt.count(pp) == 0)
            nxt[pp] = c;
          else if (nxt[pp] > c)
            nxt[pp] = c;
        };
        push(c + (tmp.size() == 1 ? 1 : 0));
        chmax(mx, c + (tmp.size() == 1 ? 1 : 0));
      }
    }
    swap(nxt, mp);
  }
  ll ans = 0;
  for (auto [p, c] : mp) {
    if (p[0] == p[1] && p[1] == a.back())
      chmax(ans, c + 1);
    else
      chmax(ans, c);
  }
  cout << ans << "\\n";

  return 0;
}