#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ll long long
#define ld long double
#define ull unsigned long long
#define ff first
#define ss second
#define pii pair<int,int>
#define pll pair<long long, long long>
#define vi vector<int>
#define vl vector<long long>
#define pb push_back
#define rep(i, b) for(int i = 0; i < (b); ++i)
#define rep2(i,a,b) for(int i = a; i <= (b); ++i)
#define rep3(i,a,b,c) for(int i = a; i <= (b); i+=c)
#define count_bits(x) __builtin_popcountll((x))
#define all(x) (x).begin(),(x).end()
#define siz(x) (int)(x).size()
#define forall(it,x) for(auto& it:(x))
using namespace __gnu_pbds;
using namespace std;
typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set;
//mt19937 mt;void random_start(){mt.seed(chrono::time_point_cast<chrono::milliseconds>(chrono::high_resolution_clock::now()).time_since_epoch().count());}
//ll los(ll a, ll b) {return a + (mt() % (b-a+1));}
const int INF = 1e9+50;
const ll INF_L = 1e18+40;
const ll MOD = 1e9+7;
const int maxn = 1000'001;
int n;
vi graph[maxn];
set<int> out_edges[maxn];
int cnt[maxn];
int my_bad[maxn];
bool is_in[maxn];
bool is_in_c[maxn];
int rep_[maxn];
int cur_not_good;
int four = -1;
bool is_four = 1;
bool is_zero = 0;
bool is_cycle = 0;
set<int> on;
int fint(int v)
{
if(rep_[v] == v) return v;
rep_[v] = fint(rep_[v]);
return rep_[v];
}
void onion(int a, int b)
{
rep_[fint(a)] = fint(b);
}
void add_one(int v)
{
if(!is_in[v]) return;
cnt[my_bad[v]]--;
my_bad[v]++;
cnt[my_bad[v]]++;
}
void Init(int N)
{
n = N;
cnt[0] = n;
rep(i,n)
{
is_in[i] = 1;
rep_[i] = i;
}
}
vi cycle;
bool odw[maxn];
bool find_cycle(int v, int dest)
{
cycle.pb(v);
if(v == dest) return 1;
odw[v] = 1;
forall(it,graph[v])
{
if(odw[it] == 0)
{
bool w = find_cycle(it,dest);
if(w) return w;
}
}
cycle.pop_back();
return 0;
}
vector<pii> opers;
void set_four(int v)
{
four = v;
rep(i,n)
{
rep_[i] = i;
graph[i] = {};
}
forall(it,opers)
{
if(it.ff == v || it.ss == v) continue;
if(fint(it.ff) == fint(it.ss))
{
is_four = 0;
}
graph[it.ff].pb(it.ss);
graph[it.ss].pb(it.ff);
onion(it.ff,it.ss);
if(siz(graph[it.ff]) > 2 || siz(graph[it.ss]) > 2)
{
is_four = 0;
}
}
}
void Link(int A, int B)
{
opers.pb({A,B});
if(is_zero) return;
if(four != -1)
{
if(A == four || B == four) return;
if(fint(A) == fint(B))
{
is_four = 0;
return;
}
graph[A].pb(B);
graph[B].pb(A);
onion(A,B);
if(siz(graph[A]) > 2 || siz(graph[B]) > 2)
{
is_four = 0;
}
return;
}
if(siz(graph[A]) == 2)
{
add_one(A);
cur_not_good++;
}
if(siz(graph[B]) == 2)
{
add_one(B);
cur_not_good++;
}
if(siz(graph[A]) == 3)
{
set_four(A);
return;
}
if(siz(graph[B]) == 3)
{
set_four(B);
return;
}
graph[A].pb(B);
graph[B].pb(A);
out_edges[A].insert(B);
out_edges[B].insert(A);
if(is_cycle)
{
if(fint(A) == fint(B))
{
int is1 = (is_in_c[A] == 1);
int is2 = (is_in_c[B] == 1);
if(is1 + is2 == 0)
{
is_zero = 1;
return;
}
if(is1 + is2 == 1)
{
if(is_in[A])
{
vi to_del;
forall(it,on)
{
if(it == A) continue;
if(out_edges[it].find(B) == out_edges[it].end() || out_edges[it].find(A) == out_edges[it].end())
{
to_del.pb(it);
}
}
forall(it,to_del)
{
on.erase(on.find(it));
cnt[my_bad[it]]--;
is_in[it] = 0;
}
}
if(is_in[B])
{
vi to_del;
forall(it,on)
{
if(it == B) continue;
if(out_edges[it].find(A) == out_edges[it].end() || out_edges[it].find(B) == out_edges[it].end())
{
to_del.pb(it);
}
}
forall(it,to_del)
{
on.erase(on.find(it));
cnt[my_bad[it]]--;
is_in[it] = 0;
}
}
}
if(is1 + is2)
{
vi to_del;
forall(it,on)
{
if(it == A || it == B) continue;
cnt[my_bad[it]]--;
is_in[it] = 0;
}
forall(it,to_del) on.erase(on.find(it));
}
}
}
else
{
if(fint(A) == fint(B))
{
is_cycle = 1;
find_cycle(A,B);
rep(i,n)
{
cnt[my_bad[i]]--;
is_in[i] = 0;
}
forall(it,cycle)
{
is_in[it] = 1;
cnt[my_bad[it]]++;
on.insert(it);
is_in_c[it] = 1;
}
}
}
onion(A,B);
if(siz(graph[A]) > 2)
{
forall(it,graph[A])
{
add_one(it);
}
}
if(siz(graph[B]) > 2)
{
forall(it,graph[B])
{
add_one(it);
}
}
}
int CountCritical()
{
// cerr << is_zero << " " << four << " " << cnt[cur_not_good] << " " << is_cycle << " ans\n";
if(is_zero) return 0;
if(four != -1)
{
if(is_four) return 1;
return 0;
}
return cnt[cur_not_good];
}
