#include <iostream>
#include <map>
#include <vector>
#define ll long long
using namespace std;
map <ll, ll> mp;
vector <ll> adj[1000000], V;
ll n, x, y, tot, P[1000000], cyc[1000000], deg[1000000];
ll dsu(ll u) {
if (P[u] == u) return u;
else return P[u] = dsu(P[u]);
}
void Init(int N_) {
n = N_;
tot = 0;
mp.clear();
for (int i=0; i<n; ++i) {
adj[i].clear();
P[i] = i;
++mp[i];
}
}
bool dfs(ll u, ll p, ll x) {
bool res = 0;
for (auto v : adj[u]) {
if (v != p) {
if (v != x && V.empty()) res |= dfs(v, u, x);
else {
if (mp.count(u)) V.push_back(u);
return 1;
}
}
}
if (res && mp.count(u)) V.push_back(u);
return res;
}
void Link(int A, int B) {
if (mp.empty()) return;
++deg[A], ++deg[B];
adj[A].push_back(B);
adj[B].push_back(A);
x = dsu(A), y = dsu(B);
if (x == y) {
++cyc[x];
++tot;
if (cyc[x] == 1) {
V.clear();
dfs(A, -1, A);
mp.clear();
for (auto u : V) ++mp[u];
}
}
else {
P[x] = y;
if (cyc[x] && cyc[y]) {
mp.clear();
return;
}
cyc[y] += cyc[x];
}
if (deg[A] > 3) {
if (mp.count(A)) {
mp.clear();
++mp[A];
}
else mp.clear();
}
else if (deg[A] == 3) {
V.clear();
if (mp.count(A)) V.push_back(A);
for (auto v : adj[A]) {
if (mp.count(v)) V.push_back(v);
}
mp.clear();
for (auto u : V) ++mp[u];
}
if (deg[B] > 3) {
if (mp.count(B)) {
mp.clear();
++mp[B];
}
else mp.clear();
}
else if (deg[B] == 3) {
V.clear();
if (mp.count(B)) V.push_back(B);
for (auto v : adj[B]) {
if (mp.count(v)) V.push_back(v);
}
mp.clear();
for (auto u : V) ++mp[u];
}
if (tot > 1) {
V.clear();
for (auto [x, y] : mp) {
if (deg[x] >= 3) V.push_back(x);
}
mp.clear();
for (auto u : V) ++mp[u];
}
}
int CountCritical() {
return mp.size();
}
