#include "simurgh.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define MASK(i) (1ULL << (i))
#define GETBIT(mask, i) (((mask) >> (i)) & 1)
#define ALL(v) (v).begin(), (v).end()
ll max(ll a, ll b){return (a > b) ? a : b;}
ll min(ll a, ll b){return (a < b) ? a : b;}
ll gcd(ll a, ll b){return __gcd(abs(a), abs(b));}
ll lcm(ll a, ll b){return abs(a) / gcd(a, b) * abs(b);}
ll LASTBIT(ll mask){return (mask) & (-mask);}
int pop_cnt(ull mask){return __builtin_popcountll(mask);}
int ctz(ull mask){return __builtin_ctzll(mask);}
int logOf(ull mask){return 63 - __builtin_clzll(mask);}
// mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
template <class T1, class T2>
bool maximize(T1 &a, T2 b){
if (a < b) {a = b; return true;}
return false;
}
template <class T1, class T2>
bool minimize(T1 &a, T2 b){
if (a > b) {a = b; return true;}
return false;
}
template <class T>
void printArr(T container, string separator = " ", string finish = "\n", ostream &out = cout){
for(auto item: container) out << item << separator;
out << finish;
}
template <class T>
void remove_dup(vector<T> &a){
sort(ALL(a));
a.resize(unique(ALL(a)) - a.begin());
}
namespace Sub{
struct DSU{
int n;
vector<int> parent, sz;
DSU(int _n){
n = _n;
parent.resize(n); sz.resize(n, 1);
for(int i = 0; i<n; ++i) parent[i] = i;
}
int find_set(int u){return (u == parent[u]) ? u : (parent[u] = find_set(parent[u]));}
bool same_set(int u, int v){return find_set(u) == find_set(v);}
bool join_set(int u, int v){
u = find_set(u), v = find_set(v);
if (u != v){
if (sz[u] < sz[v]) swap(u, v);
parent[v] = u;
sz[u] += sz[v];
return true;
}
return false;
}
int get_size(int u){return sz[find_set(u)];}
};
const int N = 505;
vector<pair<int, int>> graph[N];
pair<int, int> parent[N];
int h[N];
void reset(int n){
for(int i = 0; i < n; ++i) {
graph[i].clear();
h[i] = 0;
parent[i] = make_pair(0, 0);
}
}
void dfs(int u, int p){
if (u == p) h[u] = 1;
else h[u] = h[p] + 1;
for(pair<int, int> v: graph[u]) if (v.first != p){
parent[v.first] = make_pair(u, v.second);
dfs(v.first, u);
}
}
vector<int> solve(int n, vector<int> U, vector<int> V){
int m = U.size();
reset(n);
vector<int> spanning_tree;
DSU mst(n);
for(int i = 0; i < m; ++i){
if (mst.join_set(U[i], V[i])){
graph[U[i]].push_back(make_pair(V[i], i));
graph[V[i]].push_back(make_pair(U[i], i));
spanning_tree.push_back(i);
}
}
int og_cnt = count_common_roads(spanning_tree);
dfs(0, 0);
vector<int> cost(m, -1);
vector<int> of_spanning_tree(m);
for(int i: spanning_tree){
of_spanning_tree[i] = true;
}
for(int i = 0; i < m; ++i) if (!of_spanning_tree[i]){
vector<int> known_edges, unknown_edges;
int u = U[i], v = V[i];
while(u != v){
if (h[u] < h[v]) swap(u, v);
int e = parent[u].second;
if (cost[e] == -1) unknown_edges.push_back(e);
else known_edges.push_back(e);
u = parent[u].first;
}
if (unknown_edges.empty()) continue;
if (known_edges.size()){
int j = known_edges.back();
DSU mst(n);
vector<int> cur_spanning_tree;
cur_spanning_tree.push_back(i);
mst.join_set(U[j], V[j]);
for(int k: spanning_tree) if (k != j){
if (mst.join_set(U[k], V[k]))
cur_spanning_tree.push_back(k);
}
int cur_cnt = count_common_roads(cur_spanning_tree);
cost[i] = cost[j] + cur_cnt - og_cnt;
for(int j: unknown_edges){
DSU mst(n);
vector<int> cur_spanning_tree;
cur_spanning_tree.push_back(i);
mst.join_set(U[j], V[j]);
for(int k: spanning_tree) if (k != j){
if (mst.join_set(U[k], V[k]))
cur_spanning_tree.push_back(k);
}
int cur_cnt = count_common_roads(cur_spanning_tree);
cost[j] = cost[i] - cur_cnt + og_cnt;
}
}
else{ // covering no edge wtf
vector<int> diff;
for(int j: unknown_edges){
DSU mst(n);
vector<int> cur_spanning_tree;
cur_spanning_tree.push_back(i);
mst.join_set(U[j], V[j]);
for(int k: spanning_tree) if (k != j){
if (mst.join_set(U[k], V[k]))
cur_spanning_tree.push_back(k);
}
int cur_cnt = count_common_roads(cur_spanning_tree);
diff.push_back(cur_cnt - og_cnt);
}
pair<int,int> range = make_pair(1, -1);
for(int i: diff){
minimize(range.first, i);
maximize(range.second, i);
}
if (range == make_pair(0, 0)){
cost[i] = 0;
for(int j: unknown_edges) cost[j] = 0;
}
else if (range.second == 1){
cost[i] = 1;
for(int j = 0; j < (int) unknown_edges.size(); ++j)
cost[unknown_edges[j]] = 1 - diff[j];
}
else{
cost[i] = 0;
for(int j = 0; j < (int) unknown_edges.size(); ++j)
cost[unknown_edges[j]] = -diff[j];
}
}
}
for(int i = 0; i < m; ++i) if (cost[i] == -1 && of_spanning_tree[i]) // bridge
cost[i] = 1;
while(true){
DSU mst(n);
vector<int> pending;
for(int i = 0; i < m; ++i) if (cost[i] == -1){
if (mst.join_set(U[i], V[i])){
pending.push_back(i);
}
}
if (pending.empty()) break;
vector<int> cur_spanning_tree = pending;
int cur_cost = 0;
for(int i: spanning_tree) {
if (mst.join_set(U[i], V[i])){
cur_spanning_tree.push_back(i);
cur_cost -= cost[i];
}
}
cur_cost += count_common_roads(cur_spanning_tree);
int last = -1;
for(int i: pending) cost[i] = 0;
for(int it = 1; it <= cur_cost; ++it){
int l = last + 1, r = pending.size() - (cur_cost - it) - 1;
while(l < r){
int mid = (l + r) >> 1;
vector<int> cur_spanning_tree;
for(int i = 0; i <= mid; ++i) {
cur_spanning_tree.push_back(pending[i]);
}
int cur_cost = 0;
for(int i: spanning_tree) {
if (mst.join_set(U[i], V[i])){
cur_spanning_tree.push_back(i);
cur_cost -= cost[i];
}
}
cur_cost += count_common_roads(cur_spanning_tree);
if (cur_cost >= it) r = mid;
else l = mid + 1;
}
cost[pending[l]] = 1;
last = l;
}
}
vector<int> ans;
for(int i = 0; i < m; ++i) if (cost[i]) ans.push_back(i);
return ans;
}
}
vector<int> find_roads(int n, vector<int> u, vector<int> v){
return Sub::solve(n, u, v);
}
// int main(void){
// ios::sync_with_stdio(0);cin.tie(0); cout.tie(0);
// clock_t start = clock();
// cerr << "Time elapsed: " << clock() - start << " ms!\n";
// return 0;
// }
