#include <bits/stdc++.h>
using namespace std;
namespace good{
vector<vector<int>> g;
int n;
vector<int> deg;
void Init(int N){
n = N;
g.resize(n);
deg.assign(n, 0);
}
vector<int> cc, vis;
int cyc = 0;
void dfs(int v, int p, int gg = 1){
vis[v] = 1;
if(gg) cc.push_back(v);
for(int u: g[v]){
if(!vis[u]) dfs(u, v, gg);
else if(vis[u] == 1 && u != p){
cyc = 1;
}
}
}
int CountCritical(){
vis.assign(n, 0);
int ans = 0;
int cnt = 0;
int has = 0;
int d4 = 0;
for(int i = 0; i < n; i++){
cnt += deg[i] >= 3;
if(d4 && deg[i] > 3) return 0;
d4 |= deg[i] > 3;
}
for(int i = 0; i < n; i++) if(!vis[i]){
cc.clear();
cyc = 0;
dfs(i, -1);
int t3 = 0;
for(int v: cc){
if(deg[v] >= 3) t3 = 1;
}
if(t3 || cyc){
if(has) return 0;
has = 1;
ans = 0;
int mx = 0;
for(int v: cc){
mx = max(mx, deg[v]);
}
if(mx == 2) ans += cc.size();
else{
int nw = 0;
set<int> st;
for(int v: cc){
st.insert(v);
}
for(int v: cc) if(deg[v] == mx){
set<int> stn;
if(st.count(v)) stn.insert(v);
for(int u: g[v]){
if(st.count(u)) stn.insert(u);
}
st = stn;
}
for(int v: st) if(deg[v] == mx || mx == 3){
for(int x: cc){
vis[x] = 0;
}
vis[v] = 2;
cyc = 0;
for(int x: cc) if(!vis[x]){
dfs(x, -1, 0);
}
if(cyc == 0){
int t = cnt - (deg[v] >= 3);
for(int u: g[v]){
t -= (deg[u] == 3);
}
nw += (t == 0);
}
}
if(nw == 0) return 0;
else ans += nw;
}
}else{
if(!has){
int nw = 0;
int hv = 0;
for(int v: cc){
int t = cnt - (deg[v] >= 3);
hv |= deg[i] >= 3;
for(int u: g[v]){
t -= (deg[u] == 3);
}
nw += (t == 0);
}
ans += nw;
}
}
}
return ans;
}
void Link(int a, int b){
g[a].push_back(b);
g[b].push_back(a);
deg[a]++;
deg[b]++;
}
};
namespace bads{
struct ufds{
vector<int> sz, par;
ufds(){}
ufds(int n): sz(n, 1), par(n){
iota(par.begin(), par.end(), 0);
}
int find(int a){
return par[a] == a ? a : par[a] = find(par[a]);
}
int unite(int a, int b){
a = find(a), b = find(b);
if(a == b) return 0;
if(sz[a] < sz[b]) swap(a, b);
par[b] = a;
sz[a] += sz[b];
return 1;
}
};
set<int> ans;
vector<vector<int>> g, tree;
vector<int> deg;
int n;
ufds ds;
int bad = 0;
int d4 = 0;
void Init(int N){
n = N;
g.resize(n);
tree.resize(n);
deg.resize(n);
for(int i = 0; i < n; i++){
ans.insert(i);
}
ds = ufds(n);
}
void proc(int a, int add = 1){
if(deg[a] == 4){
if(add){
d4++;
if(d4 == 2) bad = 1;
}
if(!ans.count(a)) ans = {};
else ans = {a};
}else if(deg[a] == 3){
set<int> nans;
if(ans.count(a)) nans.insert(a);
for(int u: g[a]){
if(ans.count(u)) nans.insert(u);
}
ans = nans;
}
}
int dfs4(int v, int p, vector<int> &vis){
vis[v] = 2;
for(int u: g[v]){
if(!vis[u]){
if(dfs4(u, v, vis)) return 1;
}
else if(vis[u] == 2 && u != p){
return 1;
}
}
return 0;
}
int cyc = 0;
int CountCritical(){
if(bad) return 0;
else{
for(int x: ans) if(deg[x] > 2){
vector<int> vis(n);
vis[x] = 1;
for(int i = 0; i < n; i++) if(vis[i] == 0){
assert(!dfs4(i, -1, vis));
}
}
return ans.size();
}
}
vector<int> path;
int dfs(int v, int p, int x){
path.push_back(v);
if(v == x) return 1;
for(int u: tree[v]) if(u != p){
if(dfs(u, v, x)) return 1;
}
path.pop_back();
return 0;
}
void dfs2(int v, set<int> &vis){
if(ans.count(v)) return;
vis.insert(v);
for(int u: g[v]) if(!vis.count(u)){
dfs2(u, vis);
}
}
int dfs3(int v, set<int> &v1, set<int> &v2){
if(ans.count(v)) return 0;
if(v1.count(v)) return 1;
v2.insert(v);
for(int u: g[v]) if(!v2.count(u)){
if(dfs3(u, v1, v2)) return 1;
}
return 0;
}
void Link(int a, int b){
if(bad) return;
int res = ds.unite(a, b);
deg[a]++, deg[b]++;
g[a].push_back(b);
g[b].push_back(a);
proc(a), proc(b);
if(!res){
if(!cyc){
dfs(a, -1, b);
ans = {};
for(int x: path){
ans.insert(x);
}
for(int i = 0; i < n; i++){
proc(i, 0);
}
cyc = 1;
}else{
if(ans.size() >= 3) bad = 1;
g[a].pop_back();
g[b].pop_back();
set<int> v1, v2;
dfs2(a, v1);
if(dfs3(b, v1, v2)){
bad = 1;
}
g[a].push_back(b);
g[b].push_back(a);
}
}else{
tree[a].push_back(b);
tree[b].push_back(a);
}
}
}
void Init(int N){
good::Init(N);
bads::Init(N);
}
void Link(int a, int b){
good::Link(a, b);
bads::Link(a, b);
}
int CountCritical(){
if(bads::cyc) return good::CountCritical();
else return bads::CountCritical();
}
