#include <bits/stdc++.h>
using namespace std;
using pii = pair<int, int>;
const int N = 1e6+10;
int n;
set<int> G[N];
vector<pii> E;
// maintaining list of test nodes
int c02;
set<int> d3, d4;
inline void movenode(int u, int a, int b)
{
if (a <= 2) --c02;
if (a == 3) d3.erase(u);
if (a >= 4) d4.erase(u);
if (b <= 2) ++c02;
if (b == 3) d3.insert(u);
if (b >= 4) d4.insert(u);
}
inline set<int> testnodes()
{
if (d3.size() == 0 && d4.size() == 0) return set<int>();
if (d4.size() > 0) return d4;
set<int> ans = d3;
for (auto u : d3) {
for (auto v : G[u])
ans.insert(v);
}
return ans;
}
inline bool cancut(int u) {
if (d4.size() > 0) return d4.count(u);
if (d3.size() > 0) return d3.count(u);
return false;
}
// disjoint set
int par[N];
bool mergefail = false;
int root(int u) {
if (par[u] == u) return u;
return par[u] = root(par[u]);
}
inline void merge(int u, int v) {
u = root(u), v = root(v);
if (u == v) mergefail = true;
else par[u] = v;
}
/*inline void builddsu() {
mergefail = false;
for (int u = 0; u < n; ++u)
par[u] = u;
for (auto e : E) {
int u = e.first, v = e.second;
if (!cancut(u) && !cancut(v))
merge(u, v);
}
}
int _np[N], _nv[N], tick;
inline int &np(int u) {
if (_nv[u] != tick) {
_np[u] = par[u];
_nv[u] = tick;
}
return _np[u];
}
int newroot(int u) {
if (np(u) == u) return u;
return np(u) = newroot(np(u));
}
inline bool newmerge(int u, int v) {
u = newroot(u), v = newroot(v);
if (u == v) return false;
np(u) = v;
return true;
}*/
// testing system:
bool checkcycle(int x)
{
mergefail = false;
for (int u = 0; u < n; ++u)
par[u] = u;
for (auto e : E) {
int u = e.first, v = e.second;
if (u == x || v == x) continue;
merge(u, v);
if (mergefail) return false;
}
return true;
}
bool dead[N];
bool test(int u)
{
if (dead[u]) return false;
movenode(u, G[u].size(), 0);
for (auto v : G[u])
movenode(v, G[v].size(), G[v].size()-1);
//++tick;
bool ans = d3.size() == 0 && d4.size() == 0 && checkcycle(u);
movenode(u, 0, G[u].size());
for (auto v : G[u])
movenode(v, G[v].size()-1, G[v].size());
if (!ans) dead[u] = true;
return ans;
}
// problems:
void Init(int n) {
::n = n;
}
void Link(int a, int b) {
E.emplace_back(a, b);
movenode(a, G[a].size(), G[a].size()+1);
movenode(b, G[b].size(), G[b].size()+1);
G[a].insert(b);
G[b].insert(a);
}
int mnans = 1e9;
int CountCritical() {
if (mnans == 0 || d4.size() > 1 || d3.size() > 4)
return mnans = 0;
if (d3.size() == 0 && d4.size() == 0 && checkcycle(-1))
return mnans = n;
int cnt = 0;
for (int u = 0; u < n; ++u) if (test(u)) ++cnt;
return mnans = cnt;
}
