明显同一行的横天门、同一列的纵寰门都是互达的，所以可以将其合并为一个点，自由门按题意要求建边
Tarjan缩一波点之后建出新图，在DAG上DP找最长链即可
#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <cctype>
#include <vector>
#include <functional>
#include <algorithm>
#include <queue>
#include <set>
#include <cstdlib>
#include <ext/hash_map>
#define eps 1e-8
#include <ext/hash_set>#define LL long long
#define db doublenamespace __gnu_cxx {template<> struct hash< std::string > {size_t operator()( const std::string& x ) const {return hash< const char* >()( x.c_str() );}};
}namespace __gnu_cxx {template<> struct hash<long long> {size_t operator()(long long x) const {return (unsigned) x;}};
}using namespace std;
using namespace __gnu_cxx;#define LL long long
#define db doubletemplate <typename T> inline void CheckMax(T &a, T &b) {a = a > b ? a : b;
}template <typename T> inline void CheckMin(T &a, T &b) {a = a < b ? a : b;
}template <typename T> inline void read(T &x) {int ch = getchar();bool fg = false;for (x = 0; !isdigit(ch); ch = getchar()) {if (ch == '-') {fg = true;}}for (; isdigit(ch); ch = getchar()) {x = x * 10 + ch - '0';}if (fg) {x = -x;}
}const int MAXN = 100010;
const int MAXE = 500200;
const int MAXB = 20;
const int INF = 0x3f3f3f3f;struct Edge {int to, nxt;Edge() {}Edge(int _to, int _nxt) : to(_to), nxt(_nxt) {}
}E[MAXE];int h[MAXN], ins[MAXN], dfn[MAXN], low[MAXN], Stack[MAXN], belong[MAXN];
int Clock_t, cnt, Ins, SCC, sz[MAXN];inline void add_edge(int x, int y) {E[++cnt] = Edge(y, h[x]), h[x] = cnt;
}void Tarjan(int x) {dfn[x] = low[x] = ++Clock_t;Stack[++Ins] = x;ins[x] = 1;for(int i = h[x]; ~i; i = E[i].nxt) {int to = E[i].to;if(!dfn[to]) {Tarjan(to);low[x] = min(low[x], low[to]);}else if(ins[to])low[x] = min(low[x], dfn[to]);}if(low[x] == dfn[x]) {SCC++;int i = 0;do {i = Stack[Ins --];ins[i] = 0;belong[i] = SCC;sz[SCC]++;}while(i != x);}return ;
}void init() {SCC = Clock_t = cnt = Ins = 0;memset(dfn, 0, sizeof(dfn));memset(ins, 0, sizeof(ins));memset(belong, 0, sizeof(belong));memset(h, -1, sizeof(h));
}int n, m, R, C, totnode, Ans;
int typ[MAXN];
int dx[12] = {0, 1, 0, -1, 1, 1, -1, -1};
int dy[12] = {1, 0, -1, 0, 1, -1, 1, -1};
int in[MAXN], out[MAXN], vis[MAXN];
vector<int>rr[MAXN * 10], cc[MAXN * 10], ff;
int fir[MAXN * 10][2][5];
pair<int, int> Pos[MAXN];
hash_map<long long, int>Mp;namespace DP {struct Edge {int to, nxt;Edge() {}Edge(int _to, int _nxt) : to(_to), nxt(_nxt) {}}E[MAXE];int h[MAXN], cnt, dep[MAXN];int pos[MAXN];inline void add_edge(int x, int y) {E[++cnt] = Edge(y, h[x]), h[x] = cnt;}void Init() {memset(h, 0, sizeof(h)); cnt = 0;memset(dep, 0, sizeof(dep)); }void solve(int x) {vis[x] = 1;for(int i = h[x]; i; i = E[i].nxt) {int v = E[i].to;if(!vis[v]) solve(v);CheckMax(dep[x], dep[v]);}dep[x] += sz[x];CheckMax(Ans, dep[x]);return ;}
}#define Index(i ,j) (i - 1) * R + jvoid build() {for(int i = 1; i <= R; i++) {if(fir[i][0][1]) {int x = fir[i][0][1];for(int j = 0; j < (int) rr[i].size(); j++) {int v = rr[i][j];if(v == x) continue;if(typ[v] == 1) {add_edge(x, v);add_edge(v, x);}else add_edge(x, v);}}}for(int i = 1; i <= C; i++) {if(fir[i][1][2]) {int x = fir[i][1][2];for(int j = 0; j < (int) cc[i].size(); j++) {int v = cc[i][j];if(v == x) continue;if(typ[v] == 2) {add_edge(x, v);add_edge(v, x);}else add_edge(x, v);}}}for(int i = 0; i < (int) ff.size(); i++) {int v = ff[i];long long x = Pos[v].first, y = Pos[v].second;for(int j = 0; j < 8; j++) {long long fx = x + dx[j], fy = y + dy[j];if(Mp[Index(fx, fy)]) {add_edge(v, Mp[Index(fx, fy)]);}}}
}signed main() {read(n), read(R), read(C);init();for(int i = 1; i <= n; i++) {long long x, y;int p;read(x), read(y), read(p);Mp[(x - 1) * R + y] = ++totnode;Pos[totnode] = make_pair((int)x, (int)y);rr[x].push_back(totnode);cc[y].push_back(totnode);if(!fir[x][0][p]) fir[x][0][p] = totnode;if(!fir[y][1][p]) fir[y][1][p] = totnode;typ[totnode] = p;if(p == 3) ff.push_back(totnode);}build();for(int i = 1; i <= totnode; i++) {if(!dfn[i]) {Tarjan(i);}}for(int x = 1; x <= totnode; x++) {for(int i = h[x]; ~i; i = E[i].nxt) {int v = E[i].to;if(belong[x] != belong[v]) {in[belong[v]]++;out[belong[x]]++;DP::add_edge(belong[x], belong[v]);}}}for(int i = 1; i <= SCC; i++) {if(!vis[i]) {DP::solve(i);}}printf("%d\n", Ans);return 0;
}