#include "simurgh.h"
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define eb emplace_back
#define pb push_back
#define ft first
#define sd second
#define pi pair<int, int>
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define dbg(...) dbg_out(__VA_ARGS__)
using ll = long long;
using ld = long double;
using namespace std;
using namespace __gnu_pbds;
//Constants
const ll INF = 5 * 1e18;
const int IINF = 2 * 1e9;
const ll MOD = 1e9 + 7;
// const ll MOD = 998244353;
const ll dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const ld PI = 3.14159265359;
//Templates
template<typename A, typename B> ostream& operator<<(ostream &os, const pair<A, B> &p) {return os << '(' << p.first << ", " << p.second << ')';}
template<typename T_container, typename T = typename enable_if<!is_same<T_container, string>::value, typename T_container::value_type>::type> ostream& operator<<(ostream &os, const T_container &v) {os << '['; string sep; for (const T &x : v) os << sep << x, sep = ", "; return os << ']';}
void dbg_out() {cerr << endl;}
template<typename Head, typename... Tail> void dbg_out(Head H, Tail... T) { cerr << H << ' '; dbg_out(T...); }
template<typename T> void mins(T& x, T y) {x = min(x, y);}
template<typename T> void maxs(T& x, T y) {x = max(x, y);}
template<typename T> using oset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename T> using omset = tree<T, null_type, less_equal<T>, rb_tree_tag, tree_order_statistics_node_update>;
vector<int> find_roads(int n, vector<int> u, vector<int> v) {
int m = u.size();
vector<vector<pi>> e(n);
for (int i = 0; i < m; i++) {
e[u[i]].pb({v[i], i});
e[v[i]].pb({u[i], i});
}
vector<bool> take(m + 5, false); vector<bool> vis(n, false);
function<void(int, int)> dfs_build = [&](int f, int p) {
vis[f] = true;
for (const auto &[to, id] : e[f]) {
if (!vis[to]) {
take[id] = true;
dfs_build(to, f);
}
}
};
dfs_build(0, -1);
vector<int> cycle, col(n, 0), par(n, -1);
function<bool(int, int)> dfs_cycle = [&](int f, int p) {
col[f] = 1;
for (const auto &[to, id] : e[f]) {
if (!take[id] || to == p) continue;
if (col[to] == 1) {
int cur = f;
cycle.pb(id);
while (cur != to) {
cycle.pb(par[cur]);
if (u[par[cur]] == cur) {
cur = v[par[cur]];
} else {
cur = u[par[cur]];
}
}
return true;
} else if (col[to] == 0) {
par[to] = id;
if (dfs_cycle(to, f)) return true;
}
}
col[f] = 2;
return false;
};
int init;
{
vector<int> ar;
for (int i = 0; i < m; i++) {
if (take[i]) ar.pb(i);
}
init = count_common_roads(ar);
}
vector<int> ans(m + 5, -1);
for (int i = 0; i < m; i++) {
if (take[i]) continue;
cycle.clear();
par.assign(n, -1);
col.assign(n, 0);
take[i] = true;
dfs_cycle(0, -1);
int found = -1;
for (int edge : cycle) {
if (ans[edge] != -1) {
found = edge;
break;
}
}
if (found == -1) {
for (int edge : cycle) {
if (edge == i) continue;
take[edge] = false;
vector<int> ar;
for (int j = 0; j < m; j++) {
if (take[j]) ar.pb(j);
}
take[edge] = true;
int val = count_common_roads(ar);
if (val - init == 1) {
ans[i] = 1; ans[edge] = 0;
found = i;
break;
} else if (val - init == -1) {
ans[i] = 0; ans[edge] = 1;
found = i;
break;
}
}
if (ans[i] == -1) {
ans[i] = 0;
found = i;
}
}
for (int edge : cycle) {
if (ans[edge] != -1) continue;
int bef, aft;
{
vector<int> ar;
take[found] = false;
for (int j = 0; j < m; j++) {
if (take[j]) ar.pb(j);
}
take[found] = true;
aft = count_common_roads(ar);
}
{
vector<int> ar;
take[edge] = false;
for (int j = 0; j < m; j++) {
if (take[j]) ar.pb(j);
}
take[edge] = true;
bef = count_common_roads(ar);
}
if (ans[found] == 0) {
if (aft - bef == 1) {
ans[edge] = 1;
} else {
ans[edge] = 0;
}
} else {
if (aft - bef == 0) {
ans[edge] = 1;
} else {
ans[edge] = 0;
}
}
}
take[i] = false;
}
vector<int> ret;
for (int i = 0; i < m; i++) {
if ((take[i] && ans[i] == -1) || ans[i] == 1) {
ret.pb(i);
}
}
return ret;
}
