#include "simurgh.h"
#include <bits/stdc++.h>
using namespace std;
struct edge{
int u,v;
}e[150000];
int n,m,ch[150000],p[150000],used[150000],tin[501],tout[501],t,par[501],cur;
vector <int> ke[150000],ve;
set <int> s;
int ask(set <int> s){
vector <int> r;
for (int i:s)
r.push_back(i);
return count_common_roads(r);
}
int f(int i){
return (p[i]==i?i:p[i]=f(p[i]));
}
bool unite(int i, int j){
i=f(i);
j=f(j);
if (i==j)
return false;
p[j]=i;
return true;
}
bool create_random_spanning_tree(){
iota(p,p+n+1,0);
for (int i=0;i<n;i++)
ke[i].clear();
s.clear();
for (int i=0;i<m;i++)
if (ch[i]==1){
used[i]=unite(e[i].u,e[i].v);
if (used[i]){
ke[e[i].u].push_back(i);
ke[e[i].v].push_back(i);
s.insert(i);
}
}
if (s.size()==n-1)
return false;
for (int i=0;i<m;i++)
if (ch[i]==-1){
used[i]=unite(e[i].u,e[i].v);
if (used[i]){
ke[e[i].u].push_back(i);
ke[e[i].v].push_back(i);
s.insert(i);
}
}
cur=ask(s);
return true;
}
void dfs(int u, int parent){
tin[u]=++t;
for (int i:ke[u]){
int v=e[i].u^e[i].v^u;
if (v!=parent){
par[v]=i;
dfs(v,u);
}
}
tout[u]=t;
}
bool isancestor(int u, int v){
return (tin[u]<=tin[v]&&tout[u]>=tout[v]);
}
void get_path(int u, int v){
ve.clear();
while (!isancestor(u,v)){
ve.push_back(par[u]);
u^=e[par[u]].u^e[par[u]].v;
}
while (!isancestor(v,u)){
ve.push_back(par[v]);
v^=e[par[v]].u^e[par[v]].v;
}
}
vector <int> find_roads(int N, vector <int> u, vector <int> v){
n=N,m=u.size();
for (int i=0;i<m;i++)
e[i]={u[i],v[i]};
fill(ch,ch+m,-1);
while (create_random_spanning_tree()){
t=0;
dfs(0,0);
int restart=0;
for (int i=0;i<m;i++)
if (!used[i]&&ch[i]==-1){
get_path(u[i],v[i]);
for (int j:ve){
if (ch[j]==1){
s.erase(j);
s.insert(i);
ch[i]=1-cur+ask(s);
s.erase(i);
s.insert(j);
break;
}
}
if (ch[i]==0)
continue;
if (ch[i]==1){
restart=1;
break;
}
int mx=-1;
for (int j:ve){
s.erase(j);
s.insert(i);
ch[j]=ask(s)-cur;
mx=max(mx,ch[j]);
s.erase(i);
s.insert(j);
}
if (mx==1){
ch[i]=1;
restart=1;
for (int j:ve)
ch[j]^=1;
break;
}
ch[i]=0;
for (int j:ve)
ch[j]=-ch[j];
restart=1;
break;
}
if (!restart)
break;
}
vector <int> res;
for (int i:s)
res.push_back(i);
return res;
}
