#include<bits/stdc++.h>
using namespace std;
const int N=1000050;
int n,ord[N],par[N],cyc,cycgrp[N],cn[N];
vector<int> must,adj[N],preord;
vector<pair<int,int>> lz;
bool failed,incyc[N],vis[N];
map<pair<int,int>,bool> hv;
void Init(int N_) {
n=N_;
failed=0;
cyc=-1;
preord=must={};
for (int i=0;i<n;i++) ord[i]=0,adj[i].clear(),par[i]=cycgrp[i]=i,incyc[i]=vis[i]=0,cn[i]=-1;
}
void checknode(int u){
if (must.empty()){
must.push_back(u);
for (int i=0;i<3;i++) must.push_back(adj[u][i]);
}else{
vector<int> nw={};
for (int i:must){
bool ok=0;
if (i==u) ok=1;
for (int j=0;j<3;j++) if (i==adj[u][j]) ok=1;
if (ok) nw.push_back(i);
}
must=nw;
if (must.empty()) failed=1;
}
}
void failnode(int u){
vector<int> nw={};
for (int i:must){
bool ok=0;
if (i==u) ok=1;
if (ok) nw.push_back(i);
}
must=nw;
if (must.empty()) failed=1;
}
int find(int u){
return (par[u]==u?u:par[u]=find(par[u]));
}
int ff(int u){
return (cycgrp[u]==u?u:cycgrp[u]=ff(cycgrp[u]));
}
void merge(int u,int v){
if (cn[ff(u)]!=-1&&cn[ff(v)]!=-1&&cn[ff(u)]!=cn[ff(v)]){
cycgrp[ff(u)]=ff(v);
cn[ff(v)]=INT_MAX;
}else if (cn[ff(u)]!=-1){
cycgrp[ff(v)]=ff(u);
}else{
cycgrp[ff(u)]=ff(v);
}
}
void dfs(int u,int v){
vis[u]=1;
preord.push_back(u);
for (int i:adj[u]){
if (i==v){
incyc[v]=1;
for (int j:preord) incyc[j]=1;
if (must.empty()){
must.push_back(v);
for (int j:preord) must.push_back(j);
}
return;
}else if (vis[i]) continue;
dfs(i,v);
}
preord.pop_back();
}
int cnt,pp[N],ecnt[N];
int fff(int u){
return (pp[u]==u?u:pp[u]=fff(pp[u]));
}
int cccnt=0;
int CountCritical() {
//for (int i:must) cerr<<i<<" ";
//cerr<<"!\n";
int ret;
if (failed) ret=0;
else if (must.size()) ret=must.size();
else ret=n;
return ret;
/*cnt=0;
for (int i=0;i<n;i++){
bool ok=1;
for (int j=0;j<n;j++) pp[j]=j,ecnt[j]=0;
for (auto j:lz){
if (j.first==i||j.second==i) continue;
if (fff(j.first)==fff(j.second)) ok=0;
ecnt[j.first]++; ecnt[j.second]++;
if (ecnt[j.first]>2||ecnt[j.second]>2) ok=0;
pp[fff(j.first)]=j.second;
if (!ok) break;
}
cnt+=ok;
}
if (ret>cnt) assert(cnt==0);
//tle cnt!=0
//re cnt=0
return ret;*/
}
void Link(int u, int v) {
hv[{u,v}]=1;
ord[u]++; ord[v]++;
adj[u].push_back(v); adj[v].push_back(u);
if (failed) goto skip;
lz.push_back({u,v});
if (ord[u]==3){
checknode(u);
}else if (ord[u]>=4){
failnode(u);
}
if (failed) goto skip;
if (ord[v]==3){
checknode(v);
}else if (ord[v]>=4){
failnode(v);
}
if (failed) goto skip;
if (find(u)==find(v)){
if (cyc==-1){
adj[u].pop_back(); adj[v].pop_back();
dfs(u,v);
adj[u].push_back(v); adj[v].push_back(u);
vector<int> nw={};
for (int i:must){
if (incyc[i]) nw.push_back(i);
}
must=nw;
if (must.empty()) failed=1;
cyc=find(u);
for (auto i:lz){
if (incyc[i.first]^incyc[i.second]){
if (incyc[i.first]){
cn[ff(i.second)]=i.first;
}else{
cn[ff(i.first)]=i.second;
}
}
if (incyc[i.first]||incyc[i.second]) continue;
if (ff(i.first)!=ff(i.second)){
merge(i.first,i.second);
}
}
}else if (find(cyc)==find(u)){
//cerr<<ff(u)<<"--"<<ff(v)<<"\n";
if (incyc[u]||incyc[v]){
if (incyc[u]&&incyc[v]){
failed=1;
}else if (incyc[u]){
if (cn[ff(v)]=INT_MAX) failed=1;
if (cn[ff(v)]!=-1) cn[ff(v)]=INT_MAX;
else cn[ff(v)]=u;
}else{
if (cn[ff(u)]=INT_MAX) failed=1;
if (cn[ff(u)]!=-1) cn[ff(u)]=INT_MAX;
else cn[ff(u)]=v;
}
}else{
//cerr<<cn[ff(u)]<<"uwuuwuw"<<cn[ff(v)]<<"\n";
if (cn[ff(u)]==INT_MAX||cn[ff(v)]==INT_MAX) failed=1;
if (!(hv[{cn[ff(u)],cn[ff(v)]}]||hv[{cn[ff(v)],cn[ff(u)]}])) failed=1;
if (ff(u)==ff(v)) failed=1;
merge(u,v);
}
}else{
failed=1;
}
}else{
par[find(u)]=v;
if (cyc!=-1){
if (!(incyc[u]||incyc[v])) merge(u,v);
else{
if (incyc[u]) swap(u,v);
if (incyc[v]){
cn[ff(u)]=v;
}
}
}
}
skip:;
//cerr<<CountCritical()<<"\n";
}
/*
9 11
0 1
1 2
2 3
3 4
4 5
3 6
5 0
6 7
6 4
5 8
8 7
*/
