This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
#define endl '\n'
#define endlfl '\n' << flush
#define quit(x) return (void)(cout << x << endl)
template<typename T> void read(T& x) { cin >> x;}
template<typename T1, typename T2> void read(pair<T1, T2>& p) { read(p.first), read(p.second);}
template<typename T> void read(vector<T>& v) { for (auto& x : v) read(x); }
template<typename T1, typename T2> void read(T1& x, T2& y) { read(x), read(y); }
template<typename T1, typename T2, typename T3> void read(T1& x, T2& y, T3& z) { read(x), read(y), read(z); }
template<typename T1, typename T2, typename T3, typename T4> void read(T1& x, T2& y, T3& z, T4& zz) { read(x), read(y), read(z), read(zz); }
template<typename T> void print(vector<T>& v) { for (auto& x : v) cout << x << ' '; cout << endl; }
#define sz(x) (int)(x.size())
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define cmin(a, b) a = min(a, b)
#define cmax(a, b) a = max(a, b)
#define YES cout << "YES" << endl
#define NO cout << "NO" << endl
#define QYES quit("YES")
#define QNO quit("NO")
// #define int long long
#define double long double
const int inf = numeric_limits<int>::max() / 4;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const int MOD = 1e9+7, LOG=25;
int n, cnt;
vector<int> par, sz;
vector<vector<int>> contains;
vector<set<int>> adj;
set<pair<int, int>> critical;
int find(int x) {
if (x==par[x]) return x;
return par[x] = find(par[x]);
}
bool same(int a, int b) {
return find(a)==find(b);
}
void merge(int a, int b) {
a = find(a), b = find(b);
if (a==b) return;
if (sz[a]<sz[b]) swap(a, b);
par[b] = a;
sz[a] += sz[b];
for (int i=1; i<4; i++) {
contains[a][i] += contains[b][i];
}
}
bool works(int a) {
a=find(a);
if (sz[a]<=2) return 1;
if (contains[a][1]==2 && contains[a][3]==0) return 1;
return 0;
}
void Init(int N_) {
n = N_;
cnt=n;
par.resize(n), sz.resize(n, 1), contains.resize(n, vector<int>(4, 0));
iota(all(par), 0);
adj.resize(n);
for (int i=0; i<n; i++) critical.insert({i, 1});
}
void Link(int a, int b) {
if (critical.empty()) return;
if (a>b) swap(a, b);
if (same(a, b) || sz(adj[a])>=2 || sz(adj[b])>=2) {
if (sz(adj[a])>=3 || sz(adj[b])>=3) {
int cnta=critical.count({a, 1})||critical.count({a, 0}), cntb=critical.count({b, 1})||critical.count({b, 0});
critical.clear();
if (sz(adj[b])<3 && cnta) critical.insert({a, 1});
else if (sz(adj[a])<3 && cntb) critical.insert({b, 1});
return;
}
if (sz(critical)==n) {
critical.clear();
for (int i=0; i<n; i++) {
if (i==a || i==b || (find(i)==find(a) && sz(adj[a])<2 && sz(adj[b])<2)) {
critical.insert({i, 1});
} else if (adj[a].count(i) || adj[b].count(i)) {
critical.insert({i, 0});
}
}
} else {
set<pair<int, int>> neww;
for (auto u: critical) {
if (u.fi==a || u.fi==b) {
neww.insert({u.fi, 1});
} else if ((adj[a].count(u.fi) || adj[b].count(u.fi))) {
neww.insert({u.fi, 0});
}
}
critical=neww;
}
merge(a, b);
contains[find(a)][sz(adj[a])]--, contains[find(b)][sz(adj[b])]--;
adj[a].insert(b), adj[b].insert(a);
contains[find(a)][sz(adj[a])]++, contains[find(a)][sz(adj[b])]++;
return;
}
merge(a, b);
contains[find(a)][sz(adj[a])]--;
contains[find(b)][sz(adj[b])]--;
adj[a].insert(b), adj[b].insert(a);
contains[find(a)][sz(adj[a])]++;
contains[find(b)][sz(adj[b])]++;
}
int CountCritical() {
return sz(critical);
}
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