#include <bits/stdc++.h>
#pragma GCC target("avx2,bmi,bmi2,popcnt,lzcnt")
using namespace std;
typedef long long ll;
#define ll int
typedef pair<int,int> pi;
typedef vector <int> vi;
typedef vector <pi> vpi;
typedef pair<pi, ll> pii;
typedef set <ll> si;
typedef long double ld;
#define f first
#define s second
#define mp make_pair
#define FOR(i,s,e) for(int i=s;i<=int(e);++i)
#define DEC(i,s,e) for(int i=s;i>=int(e);--i)
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define lbd(x, y) lower_bound(all(x), y)
#define ubd(x, y) upper_bound(all(x), y)
#define aFOR(i,x) for (auto i: x)
#define mem(x,i) memset(x,i,sizeof x)
#define fast ios_base::sync_with_stdio(false),cin.tie(0),cout.tie(0)
#define maxn 1000010
#define INF (ll)1e9
#define MOD 1000000007
typedef pair <vi, int> pvi;
typedef pair <int,pi> ipi;
typedef vector <pii> vpii;
int N;
int d[maxn], maxD;
vi st[maxn], adj[maxn],cycles[5];
vpi all_edges;
int p[maxn][5], edges[maxn][5], sz[maxn][5], ncycles[5];
vi pos;
int fl(int i, int x){
if (p[x][i] == x) return x;
return p[x][i] = fl(i, p[x][i]);
}
void add(int i, int A, int B){
if (sz[fl(i,A)][i] > sz[fl(i,B)][i]) swap(A,B);
if (fl(i, A) != fl(i,B)){
int pA = fl(i,A), pB = fl(i,B);
if (edges[pA][i] >= sz[pA][i]) ncycles[i]--;
if (edges[pB][i] >= sz[pB][i]) ncycles[i]--;
sz[pB][i] += sz[pA][i];
edges[pB][i] += edges[pA][i];
p[pA][i] = pB;
}else if (edges[fl(i,A)][i] >= sz[fl(i,A)][i]) ncycles[i]--;
edges[fl(i,B)][i]++;
if (edges[fl(i,B)][i] >= sz[fl(i,B)][i]){
ncycles[i]++; cycles[i].pb(fl(i,B));
}
}
int bigx;
int gt3 = 0;
void Init(int N_) {
N = N_;
maxD = 0;
FOR(i,0,4) FOR(j,0,N-1) p[j][i] = j,sz[j][i] = 1;
bigx = -1;
}
void Link(int A, int B) {
if (d[A] == 3) gt3++;
if (d[B] == 3) gt3++;
d[A]++; d[B]++;
st[d[A]].pb(A); st[d[B]].pb(B);
adj[A].pb(B); adj[B].pb(A);
if (pos.empty() && (d[A] == 3 || d[B] == 3)){
if (d[A] == 3){
aFOR(i, adj[A]) pos.pb(i);
pos.pb(A);
}else if (d[B] == 3){
pos.pb(B); aFOR(i, adj[B]) pos.pb(i);
}
FOR(i,0,pos.size()-1){
aFOR(j, all_edges) if (j.f != pos[i] && j.s != pos[i]) add(i,j.f,j.s);
}
}
all_edges.pb(pi(A,B));
maxD = max({maxD, d[A], d[B]});
add(4,A,B);
FOR(i,0,(int)pos.size()-1) if (A != pos[i] && B != pos[i]) add(i,A,B);
}
int CountCritical() {
if (N == 1) return 1;
if (maxD >= 4){
if (gt3 > 1) return 0;
if (st[maxD].size() == 1){
int x = st[maxD][0];
if (find(all(pos),x) == pos.end()) return 0;
int idx = find(all(pos), x) - pos.begin();
if (!cycles[idx].empty()) return 0;
aFOR(i, st[3]) if (i != x && find(all(adj[i]), x) == adj[i].end()) return 0;
return 1;
}else return 0;
}else if (maxD <= 1) return N;
else if (maxD == 3){
if (st[3].size() > 4) return 0;
int ans = 0;
FOR(i,0,pos.size()-1){
bool no = 0;
aFOR(j, st[3]) if (pos[i] != j && find(all(adj[j]), pos[i]) == adj[j].end()){
no = 1; break;
}
if (no) continue;
if (cycles[i].empty()){
ans++;
}
}
return ans;
}else{
if (ncycles[4] == 0) return N;
else if (ncycles[4] == 1) return sz[fl(4,cycles[4][0])][4];
else return 0;
}
}
