#include <iostream>
#include <vector>
#include <set>
#include <iomanip>
#include <algorithm>
#include <functional>
#include <stdio.h>
#include <cmath>
#include <queue>
#include <string>
#include <map>
#include <fstream>
#include <complex>
#include <stack>
#include <set>
#define FOR(i,n) for(int i=0;i<n;i++)
#define FORE(i,a,b) for(int i=a;i<=b;i++)
#define ll long long int
#define vi vector<int>
#define ii pair<int,int>
#define pb push_back
#define mp make_pair
#define ff first
#define ss second
#define pll pair<ll,ll>
#define cd complex<double>
#define ld long double
#define pld pair<ld,ld>
#define iii pair<ii,int>
using namespace std;
const int INF = 1e9+10;
const int MAXN = 1000*100*10+10;
const int MAXVAL = 1e9+10;
vi g[MAXN];
vector<ii> edges;
int n;
int parent[MAXN];
struct DSU{
DSU(int n){
//parent = new int[n];
FOR(i,n)parent[i] = i;
}
inline int find(int a){
if(parent[a] != a)parent[a] = find(parent[a]);
return parent[a];
}
inline void merge(int a,int b){
int pa = find(a);
int pb = find(b);
parent[pa] = pb;
}
};
void Init(int N){
n = N;//gdsu = new DSU(n);
}
void Link(int a,int b){
g[a].pb(b);
g[b].pb(a);
edges.pb({a,b});
}
inline bool isCritical(int x){
DSU dsu(n);
int deg[n];
FOR(i,n)deg[i] = 0;
for(auto e : edges){
if(e.ff == x or e.ss == x)continue;
deg[e.ff]++;
deg[e.ss]++;
if(dsu.find(e.ff) == dsu.find(e.ss)){
return 0;
}
dsu.merge(e.ff,e.ss);
}
FOR(i,n)if(deg[i] > 2)return 0;
return 1;
}
int CountCritical(){
// check first if there is atleast 1 node of degree 2 or more.
vector<ii> all;
FOR(i,n){
all.pb({g[i].size(),i});
}
sort(all.begin(), all.end());
reverse(all.begin(), all.end());
int ctr = 0;
if(all[0].ff > 2){
FOR(i,min(7,n)){
ctr += isCritical(all[i].ss);
}
return ctr;
}else{
FOR(i,n){
ctr += isCritical(i);
}
return ctr;
}
while(1);
{
//cout << "yaya" << endl;
DSU dsu(n);
for(auto e:edges){
if(dsu.find(e.ff) != dsu.find(e.ss))dsu.merge(e.ff,e.ss);
}
int ed[n];
int nd[n];
FOR(i,n)ed[i] = nd[i] = 0;
for(auto e:edges){
ed[dsu.find(e.ff)]++;
}
FOR(i,n)nd[dsu.find(i)]++;
// find how many components have cycles
vi vv;
FOR(i,n){
if(nd[i] > 0 and ed[i] >= nd[i]){
vv.pb(nd[i]);
}
}
//cout << vv.size() << endl;
if(vv.size() > 1){
//while(1);
return 0;
}else if(vv.size() == 1){
return vv[0];
}else{
return n;
}
}
/*
FOR(i,n){
ctr += isCritical(i);
}*/
}
/*
int main(){
Init(7);
cout << CountCritical() << endl;
Link(1,2);
cout << CountCritical() << endl;
Link(0,5);
cout << CountCritical() << endl;
Link(0,2);
cout << CountCritical() << endl;
Link(3,2);
cout << CountCritical() << endl;
Link(3,5);
cout << CountCritical() << endl;
Link(3,4);
cout << CountCritical() << endl;
return 0;
}*/
