#pragma GCC optimize ("O3")
#include <bits/stdc++.h>
#define pii pair<int, int>
#define piii pair<pii, int>
#define vi vector<int>
#define vvi vector<vi>
#define vpii vector<pii>
#define vvpii vector<vpii>
#define f first
#define s second
#define oo 1000000001
#define eb emplace_back
#define pb push_back
#define mpr make_pair
#define size(v) (int)v.size()
#define ln '\n'
#define ull unsigned long long
#define ll long long
#define all(v) v.begin(), v.end()
using namespace std;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
struct DSU {
int components;
vector<int>par;
DSU(){}
DSU(int n) {
par.assign(n, -1);
components = n;
}
void init(int n) {
par.assign(n, -1);
components = n;
}
int Find(int u) {
if (par[u] < 0) return u;
else return par[u] = Find(par[u]);
}
bool Union(int u, int v) {
u = Find(u);
v = Find(v);
if (u != v) {
if (par[u] > par[v]) {
swap(u, v);
}
par[u] += par[v];
par[v] = u;
--components;
return true;
} else {
return false;
}
}
};
int N, critical, cycle;
DSU dsu[4];
bool isCritical[4];
int root[4];
vpii edges;
vi deg[4];
void Init(int N_) {
N = N_;
critical = N;
cycle = 0;
for (int i = 0; i < 4; ++i) {
dsu[i].init(N);
deg[i].assign(N, 0);
root[i] = -1;
}
}
void Link(int A, int B) {
if (!critical) return;
if (root[0] == -1) {
edges.eb(mpr(A, B));
deg[0][A]++;
deg[0][B]++;
if (deg[0][A] == 3) {
root[0] = A;
} else if (deg[0][B] == 3) {
root[0] = B;
}
if (root[0] != -1) {
int id = 0;
for (pii e : edges) {
if (e.f == root[0] || e.s == root[0]) {
root[++id] = e.f + e.s - root[0];
}
}
dsu[0].init(N);
deg[0].assign(N, 0);
critical = 4;
for (int i = 0; i < 4; ++i) {
isCritical[i] = true;
for (pii e : edges) {
if (e.f != root[i] && e.s != root[i]) {
deg[i][e.f]++;
deg[i][e.s]++;
if (!dsu[i].Union(e.f, e.s) || deg[i][e.f] >= 3 || deg[i][e.s] >= 3) {
isCritical[i] = false;
--critical;
break;
}
}
}
}
} else {
if (!dsu[0].Union(A, B)) {
++cycle;
if (cycle == 1) {
critical = -dsu[0].par[dsu[0].Find(A)];
} else {
critical = 0;
}
}
}
} else {
for (int i = 0; i < 4; ++i) {
if (isCritical[i] && root[i] != A && root[i] != B) {
deg[i][A]++;
deg[i][B]++;
if (!dsu[i].Union(A, B) || deg[i][A] >= 3 || deg[i][B] >= 3) {
isCritical[i] = false;
--critical;
}
}
}
}
}
int CountCritical() {
return critical;
}
