#include "simurgh.h"
#include<bits/stdc++.h>
#define pii pair<int,int>
#define f first
#define s second
using namespace std;
const int N = 1e6 + 5;
int f[N], t[N], CNT, P[N], h[N], Nn, up[N], imp[N], p[N];
pii mn[N];
vector<int> golden;
vector<pii> V[N], adj[N], E;
vector<int> edges, x[N];
void dfs0(int u, int p) {
f[u] = 1;
for(int i = 0; i < V[u].size(); i++) {
if(V[u][i].f == p) continue;
if(!f[V[u][i].f]) {
dfs0(V[u][i].f, u); //cout << "++" << V[u][i].s << endl;
edges.push_back(V[u][i].s);
t[V[u][i].s] = 1;
}
}
}
int rem(int e1, int e2) {
vector<int> x;
for(int i = 0; i < edges.size(); i++) {
if(e1 != edges[i]) x.push_back(edges[i]);
}
x.push_back(e2);
return count_common_roads(x) - CNT;
}
void add(int a, int b, int x) {
adj[a].push_back({b, x});
adj[b].push_back({a, -x});
}
void dfs(int u, int p) {
mn[u] = {Nn + 1, 0};
P[u] = p;
if(u) h[u] = h[p] + 1; //cout << u << endl;
for(int i = 0; i < V[u].size(); i++) {
int e = V[u][i].s, v = V[u][i].f;
if(v == p) continue;
if(t[e]) {
up[v] = e;
dfs(v, u);
if(mn[v].f > h[u]) golden[e] = 1;
else add(e, mn[v].s, rem(e, mn[v].s)), imp[mn[v].s] = 1;
mn[u] = min(mn[u], mn[v]);
} else {
if(h[v] > h[u] && imp[e]) {
int x = v;
while(P[x] != u) {
x = P[x];
}
add(up[x], e, rem(up[x], e));
}
if(h[v] < h[u]) mn[u] = min(mn[u], {h[v], e});
}
}
}
int find(int u) {
return (p[u] == u ? u : p[u] = find(p[u]));
}
void merge(int u, int v) {
u = find(u), v = find(v);
p[u] = v;
}
int ask(vector<int> x, int mid) {
for(int i = 0; i < Nn; i++) {
p[i] = i;
}
vector<int> v;
for(int i = 0; i < mid; i++) v.push_back(x[i]), merge(E[x[i]].f, E[x[i]].s);
int c = 0;
for(int i = 0; i < edges.size(); i++) {
if(find(E[edges[i]].f) != find(E[edges[i]].s)) {
v.push_back(edges[i]);
merge(E[edges[i]].f, E[edges[i]].s);
c += golden[edges[i]];
}
}
return count_common_roads(v) - c;
}
std::vector<int> find_roads(int nn, std::vector<int> u, std::vector<int> vv) {
int m = u.size(); Nn = nn;
golden.resize(m);
for(int i = 0; i < m; i++) {
V[u[i]].push_back({vv[i], i});
V[vv[i]].push_back({u[i], i});
E.push_back({vv[i], u[i]});
}
dfs0(0, -1);
CNT = count_common_roads(edges);
dfs(0, -1);
vector<int> vis(m);
for(int i = 0; i < m; i++) {
if(!vis[i]) {
queue<int> q;
q.push(i);
h[i] = 0;
int mx = 0, mn = 0;
vector<int> x;
while(q.size()) {
int u = q.front(); q.pop();
mx = max(mx, h[u]); mn = min(mn, h[u]);
for(int j = 0; j < adj[u].size(); j++) {
if(vis[adj[u][j].f]) continue;
h[adj[u][j].f] = h[u] + adj[u][j].s;
vis[adj[u][j].f] = 1;
q.push(adj[u][j].f);
}
x.push_back(u);
}
if(mn == mx) continue;
for(int j = 0; j < x.size(); j++) if(h[x[j]] == mx) golden[x[j]] = 1;
}
}
for(int i = 0; i < m; i++) {
if(t[i]) continue;
x[min(u[i], vv[i])].push_back(i);
}
for(int i = 0; i < Nn; i++) {
int cn = ask(x[i], x[i].size());// cout << cn << " _ " << i << endl;
int L = 0;
for(int j = 1; j <= cn; j++) {
int l = L, r = (int)x[i].size() - 1, id = 0;
while(l <= r) {
int mid = (l + r) / 2;
if(ask(x[i], mid + 1) >= j) id = mid, r = mid - 1;
else l = mid + 1;
}
golden[x[i][id]] = 1;
L = id + 1;
}
}
vector<int> ans;
for(int i = 0; i < m; i++) if(golden[i]) ans.push_back(i);
return ans;
}
