#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define MASK(i) (1LL << (i))
#define GETBIT(mask, i) (((mask) >> (i)) & 1)
#define ALL(v) (v).begin(), (v).end()
ll max(ll a, ll b){return (a > b) ? a : b;}
ll min(ll a, ll b){return (a < b) ? a : b;}
ll gcd(ll a, ll b){return __gcd(a, b);}
ll LASTBIT(ll mask){return (mask) & (-mask);}
int pop_cnt(ll mask){return __builtin_popcountll(mask);}
int ctz(ll mask){return __builtin_ctzll(mask);}
int logOf(ll mask){return __lg(mask);}
mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
ll rngesus(ll l, ll r){return l + (ull) rng() % (r - l + 1);}
template <class T1, class T2>
bool maximize(T1 &a, T2 b){
if (a < b) {a = b; return true;}
return false;
}
template <class T1, class T2>
bool minimize(T1 &a, T2 b){
if (a > b) {a = b; return true;}
return false;
}
template <class T>
void printArr(T& container, string separator = " ", string finish = "\n"){
for(auto item: container) cout << item << separator;
cout << finish;
}
template <class T>
void remove_dup(vector<T> &a){
sort(ALL(a));
a.resize(unique(ALL(a)) - a.begin());
}
const int N = 1e6 + 69;
struct DSU{
int n;
vector<int> parent, sz, is_cycle;
int cycle_cnt, sum_cycle;
DSU(int _n){
n = _n;
parent.resize(n); sz.resize(n, 1); is_cycle.resize(n, 0);
clear();
}
void clear(){
for(int i = 0; i<n; ++i) {
parent[i] = i;
sz[i] = 1;
is_cycle[i] = 0;
}
cycle_cnt = sum_cycle = 0;
}
int find_set(int u){return (u == parent[u]) ? u : (parent[u] = find_set(parent[u]));}
bool same_set(int u, int v){return find_set(u) == find_set(v);}
bool join_set(int u, int v){
u = find_set(u), v = find_set(v);
if (u != v){
if (sz[u] < sz[v]) swap(u, v);
if (is_cycle[u]) {
cycle_cnt--;
sum_cycle -= sz[u];
}
if (is_cycle[v]) {
cycle_cnt--;
sum_cycle -= sz[v];
}
parent[v] = u;
sz[u] += sz[v];
is_cycle[u] |= is_cycle[v];
if (is_cycle[u]) {
cycle_cnt++;
sum_cycle += sz[u];
}
return true;
}
if (is_cycle[u] == 0) {
cycle_cnt++;
sum_cycle += sz[v];
}
is_cycle[u] = 1;
return false;
}
int get_size(int u){return sz[find_set(u)];}
int get_cycle_top(){
if (cycle_cnt == 0) return -1;
if (cycle_cnt >= 2) return -2;
return sum_cycle;
}
};
int n;
DSU mst(N);
int deg[N];
vector<int> graph[N];
int cur_ans;
int max_deg;
int banned_vertex;
void Init(int _N) {
n = _N;
cur_ans = n;
max_deg = 0;
banned_vertex = -1;
}
namespace Three{
vector<int> hero_party;
vector<DSU> sigma;
vector<vector<int>> deg;
vector<int> max_deg;
}
void Link(int u, int v) {
if (cur_ans == 0) return;
if (u != banned_vertex && v != banned_vertex){
mst.join_set(u, v);
deg[u]++;
deg[v]++;
graph[u].push_back(v);
graph[v].push_back(u);
maximize(max_deg, max(deg[u], deg[v]));
}
if (Three::hero_party.size() == 4){
for(int k = 0; k < 4; ++k){
int cur = Three::hero_party[k];
if (u == cur || v == cur) continue;
Three::deg[k][u]++;Three::deg[k][v]++;
Three::sigma[k].join_set(u, v);
maximize(Three::max_deg[k], max(Three::deg[k][u], Three::deg[k][v]));
}
}
if (max_deg >= 4 && banned_vertex == -1){
for(int i = 0; i < n; ++i) if (deg[i] >= 4) banned_vertex = i;
mst.clear();
for(int i = 0; i < n; ++i) for(int j: graph[i]) if (i < j){
if (i == banned_vertex || j == banned_vertex) continue;
mst.join_set(i, j);
}
for(int v: graph[banned_vertex]) {
deg[v]--;
deg[banned_vertex]--;
}
max_deg = 0;
for(int i = 0; i < n; ++i) maximize(max_deg, deg[i]);
cur_ans = 1;
}
if (banned_vertex != -1){
if (mst.get_cycle_top() != -1 || max_deg > 2) cur_ans = 0;
return;
}
int cur = mst.get_cycle_top();
if (cur == -2) cur_ans = 0;
else if (cur != -1){
minimize(cur_ans, cur);
}
if (max_deg == 3){
if (Three::hero_party.size() == 0){
int u = -1;
for(int i = 0; i < n; ++i) if (deg[i] == 3) u = i;
Three::hero_party = graph[u];
Three::hero_party.push_back(u);
for(int i = 0; i < 4; ++i) {
Three::sigma.push_back(DSU(n));
Three::deg.push_back(vector<int>(n));
}
Three::max_deg.resize(4);
for(int k = 0; k < 4; ++k){
int cur = Three::hero_party[k];
for(int i = 0; i < n; ++i) for(int j: graph[i]) if (i < j){
if (i == cur || j == cur) continue;
Three::deg[k][i]++;
Three::deg[k][j]++;
Three::sigma[k].join_set(i, j);
maximize(Three::max_deg[k], max(Three::deg[k][i], Three::deg[k][j]));
}
}
}
cur_ans = 0;
for(int i = 0; i < 4; ++i){
if (Three::max_deg[i] > 2 || Three::sigma[i].get_cycle_top() != -1) continue;
cur_ans++;
}
}
}
int CountCritical() {
return cur_ans;
}
// int main(void){
// ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
// clock_t start = clock();
// int n, l; cin >> n >> l;
// Init(n);
// for(int i = 0; i < l; ++i){
// int a; cin >> a;
// if (a == -1) cout << CountCritical() << "\n";
// else{
// int b; cin >> b;
// Link(a, b);
// }
// }
// cerr << "Time elapsed: " << clock() - start << "ms!\n";
// return 0;
// }
