#include "simurgh.h"
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ll long long
#define ld long double
#define ull unsigned long long
#define ff first
#define ss second
#define pii pair<int,int>
#define pll pair<long long, long long>
#define vi vector<int>
#define vl vector<long long>
#define pb push_back
#define rep(i, b) for(int i = 0; i < (b); ++i)
#define rep2(i,a,b) for(int i = a; i <= (b); ++i)
#define rep3(i,a,b,c) for(int i = a; i <= (b); i+=c)
#define count_bits(x) __builtin_popcountll((x))
#define all(x) (x).begin(),(x).end()
#define siz(x) (int)(x).size()
#define forall(it,x) for(auto& it:(x))
using namespace __gnu_pbds;
using namespace std;
typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set;
mt19937 mt;void random_start(){mt.seed(chrono::time_point_cast<chrono::milliseconds>(chrono::high_resolution_clock::now()).time_since_epoch().count());}
ll los(ll a, ll b) {return a + (mt() % (b-a+1));}
const int INF = 1e9+50;
const ll INF_L = 1e18+40;
const ll MOD = 1e9+7;
vector<pii> graph[501];
int val[501*501];
int edge_num[501][501];
vi end_points[501*501];
bool odw[501];
int pre[501];
int low[501];
int odw_path[501];
int cur_pre = 0;
bool bridges[501*501];
int color[501];
vi known_tree;
vi comp = {};
int n;
void dfs_low(int v, int pop)
{
pre[v] = cur_pre++;
low[v] = pre[v];
odw[v] = 1;
forall(it,graph[v])
{
if(it.ff != pop)
{
if(odw[it.ff])
{
low[v] = min(pre[it.ff],low[v]);
}
else
{
dfs_low(it.ff,v);
low[v] = min(low[v],low[it.ff]);
if(low[it.ff] == pre[it.ff])
{
bridges[it.ss] = 1;
val[it.ss] = 1;
known_tree.pb(it.ss);
}
}
}
}
}
void dfs_comp(int v)
{
comp.pb(v);
odw[v] = 1;
forall(it,graph[v])
{
if(odw[it.ff] == 0 && !bridges[it.ss])
{
dfs_comp(it.ff);
}
}
}
vi path;
bool gen_path(int v, int pop)
{
path.pb(v);
if(odw[v] == 1 && v != pop)
{
return 1;
}
if(odw[v] == 0) color[v] = 1;
forall(it,graph[v])
{
if(!bridges[it.ss] && it.ff != pop && (odw[it.ff] == 0 || v != pop) && color[it.ff] == 0)
{
if(gen_path(it.ff,v)) return 1;
}
}
path.pop_back();
return 0;
}
vi cur_p;
vi doc_path;
int ci = 0;
void dfs_path(int v, int doc)
{
cur_p.pb(v);
if(v == doc)
{
doc_path = cur_p;
return;
}
odw_path[v] = ci;
forall(it,graph[v])
{
if(odw[it.ff] == 1 && odw_path[it.ff] != ci)
{
dfs_path(it.ff,doc);
if(siz(doc_path) != 0) return;
}
}
cur_p.pop_back();
}
vi rng_tree;
void find_random_tree(int v)
{
odw_path[v] = ci;
forall(it,graph[v])
{
if(odw_path[it.ff] != ci)
{
rng_tree.pb(it.ss);
find_random_tree(it.ff);
}
}
}
void find_cycle_vals(vi edge, vi verts)
{
rng_tree = {};
ci++;
forall(it,verts) odw_path[it] = ci;
forall(it,verts) find_random_tree(it);
forall(it,edge) known_tree.pb(it);
int ke = -1;
forall(it,edge) if(val[it] != -1) ke = it;
if(ke != -1)
{
vi query_tree = rng_tree;
forall(it,edge) if(it != ke) query_tree.pb(it);
int ke_val = count_common_roads(query_tree);
rep(i,siz(edge)-1) query_tree.pop_back();
forall(it,edge)
{
if(val[it] != -1) continue;
forall(it2,edge)
{
if(it != it2) query_tree.pb(it2);
}
if(ke_val == count_common_roads(query_tree)) val[it] = val[ke];
else val[it] = val[ke] ^ 1;
rep(i,siz(edge)-1) query_tree.pop_back();
}
}
else
{
vi query_tree = rng_tree;
int max_ = -1e9;
int min_ = 1e9;
forall(it,edge)
{
if(val[it] != -1) continue;
forall(it2,edge)
{
if(it != it2) query_tree.pb(it2);
}
val[it] = count_common_roads(query_tree);
min_ = min(min_,val[it]);
max_ = max(max_,val[it]);
rep(i,siz(edge)-1) query_tree.pop_back();
}
if(min_ == max_) forall(it,edge) val[it] = 0;
else
{
forall(it,edge)
{
if(val[it] == min_) val[it] = 1;
else val[it] = 0;
}
}
}
}
int rep_[501];
int fint(int v)
{
if(rep_[v] == v) return v;
rep_[v] = fint(rep_[v]);
return rep_[v];
}
void onion(int a, int b)
{
rep_[fint(a)] = fint(b);
}
int count_forest_val(vi f)
{
rep(i,n) rep_[i] = i;
int known_sum = 0;
vi query_tree = f;
forall(it,f) onion(end_points[it][0],end_points[it][1]);
forall(it,known_tree)
{
if(fint(end_points[it][0]) != fint(end_points[it][1]))
{
known_sum += val[it];
query_tree.pb(it);
onion(end_points[it][0],end_points[it][1]);
}
}
return count_common_roads(query_tree) - known_sum;
}
vi find_roads(int N, vi u, vi v)
{
n = N;
rep(i,siz(u))
{
val[i] = -1;
end_points[i] = {v[i],u[i]};
graph[u[i]].pb({v[i],i});
graph[v[i]].pb({u[i],i});
edge_num[u[i]][v[i]] = i;
edge_num[v[i]][u[i]] = i;
}
dfs_low(0,0);
rep(i,n) odw[i] = 0;
rep(i,n)
{
if(odw[i] == 0)
{
comp = {};
dfs_comp(i);
if(siz(comp) == 1) continue;
forall(it,comp)
{
odw[it] = 0;
}
queue<int> q;
q.push(i);
odw[i] = 1;
while(!q.empty())
{
int t = q.front();
q.pop();
while(true)
{
path = {};
forall(it,comp) color[it] = 0;
gen_path(t,t);
if(siz(path) == 0) break;
ci++;
cur_p = {};
doc_path = {};
dfs_path(path.back(),path[0]);
forall(it,path)
{
if(odw[it] == 0)
{
q.push(it);
}
odw[it] = 1;
}
vi total_path = path;
total_path.pop_back();
forall(it,doc_path) total_path.pb(it);
vi cycle_edges;
rep(i,siz(total_path)-1)
{
cycle_edges.pb(edge_num[total_path[i]][total_path[i+1]]);
}
find_cycle_vals(cycle_edges,total_path);
}
}
}
}
rep(i,n)
{
vi unknown;
forall(it,graph[i])
{
if(val[it.ss] == -1) unknown.pb(it.ss);
}
int deg = count_forest_val(unknown);
if(deg == 0)
{
forall(it,graph[i])
{
if(val[it.ss] == -1) val[it.ss] = 0;
}
continue;
}
rep(j,deg)
{
vi s;
forall(it,unknown) if(val[it] == -1) s.pb(it);
while(siz(s) != 1)
{
vi left;
vi right;
rep(i,siz(s)/2) left.pb(s[i]);
rep(i,(siz(s)+1)/2) right.pb(s[siz(s)/2 + i]);
if(count_forest_val(left) > 0) s = left;
else s = right;
}
val[s[0]] = 1;
}
}
vi ans;
rep(i,siz(u))
{
if(val[i] == 1)
{
ans.pb(i);
}
}
return ans;
}
