#include "simurgh.h"
#include <bits/stdc++.h>
using namespace std;
struct edge{
int u,v;
}e[150000];
int n,m,ch[150000],low[501],tin[501],tout[501],t,par[501],cur,p[501];
vector <int> ve,res;
set <int> s,ke[501];
int ask(set <int> s){
vector <int> r;
for (int i:s)
r.push_back(i);
return count_common_roads(r);
}
void dfs(int u, int parent){
tin[u]=low[u]=++t;
for (int i:ke[u]){
int v=e[i].u^e[i].v^u;
if (v!=parent){
if (!tin[v]){
s.insert(i);
par[v]=i;
dfs(v,u);
low[u]=min(low[u],low[v]);
if (low[v]==tin[v])
ch[i]=1;
}
else
low[u]=min(low[u],tin[v]);
}
}
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;
}
}
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;
}
int calc(set <int> s2){
iota(p,p+n,0);
for (int i:s2)
unite(e[i].u,e[i].v);
int cnt=0;
for (int i:s)
if (unite(e[i].u,e[i].v)){
s2.insert(i);
cnt+=ch[i];
}
return ask(s2)-cnt;
}
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]};
ke[u[i]].insert(i);
ke[v[i]].insert(i);
}
fill(ch,ch+m,-1);
dfs(0,0);
cur=ask(s);
for (int i=0;i<m;i++)
if (s.find(i)==s.end()){
get_path(u[i],v[i]);
int c=1;
for (int j:ve)
if (ch[j]==-1)
c=0;
if (c)
continue;
for (int j:ve){
if (ch[j]!=-1){
s.erase(j);
s.insert(i);
ch[i]=(ch[j]?1-cur+ask(s):ask(s)-cur);
s.erase(i);
s.insert(j);
break;
}
}
if (ch[i]!=-1){
for (int j:ve)
if (ch[j]==-1){
s.erase(j);
s.insert(i);
ch[j]=(ch[i]?1+cur-ask(s):cur-ask(s));
s.erase(i);
s.insert(j);
}
continue;
}
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;
for (int j:ve)
ch[j]^=1;
continue;
}
ch[i]=0;
for (int j:ve)
ch[j]=-ch[j];
}
vector <int> tmp;
set <int> S;
for (int i=0;i<n;i++){
int deg=calc(ke[i]);
while (deg){
tmp.clear();
for (int j:ke[i])
tmp.push_back(j);
int l=0,r=tmp.size()-1,kq=-1;
while (l<=r){
int mid=(l+r)>>1;
S.clear();
for (int i=0;i<=mid;i++)
S.insert(tmp[i]);
if (calc(S)==deg){
kq=tmp[mid];
r=mid-1;
}
else
l=mid+1;
}
res.push_back(kq);
ke[u[kq]].erase(kq);
ke[v[kq]].erase(kq);
deg--;
}
}
return res;
}
