// ~Be name khoda~ //
#include "meetings.h"
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
#define pb push_back
#define mp make_pair
#define all(x) x.begin(), x.end()
#define fi first
#define se second
#define cl clear
#define endll '\n'
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const int maxn = 1e6 + 10;
const int maxn5 = 5e5 + 10;
const int maxnt = 1.2e6 + 10;
const int maxn3 = 1e3 + 10;
const int mod = 1e9 + 7;
const ll inf = 2e18;
int n, per[maxn5];
vector <int> adj[maxn5], tmp, av;
int mx[maxn5], sz[maxn5], rev[maxn5];
bool rem[maxn5], mark[maxn5];
int lev = 0;
inline void remo(int a, int b){
tmp.clear();
for(auto u : adj[a])
if(u != b) tmp.pb(u);
adj[a].clear();
for(auto u : tmp)
adj[a].pb(u);
return;
}
inline void dfs(int v, int par){
sz[v] = 1;
mx[v] = 0;
av.pb(v);
for(auto u : adj[v]) if(u != par && !rem[u]){
dfs(u, v);
mx[v] = max(mx[v], sz[u]);
sz[v] += sz[u];
}
return;
}
inline void add(int r, int v){
lev++;
//cout << "adding " << r << ' ' << v << endl;
av.clear();
dfs(r, -1);
int c = r;
for(auto u : av)
if(max(mx[u], int(av.size()) - sz[u]) < max(mx[c], int(av.size()) - sz[c]))
c = u;
int sub = -1;
//cout << "centroid " << c << endl;
assert(lev <= 11);
for(auto uu : adj[c]) if(!rem[uu]){
int u = uu;
int t = Query(per[c], per[u], per[v]);
t = rev[t];
if(t == v){
//cout << "right " << u << endl;
remo(u, c);
remo(c, u);
adj[u].pb(v);
adj[c].pb(v);
adj[v].pb(u);
adj[v].pb(c);
return;
}
else if(t == u){
sub = u;
break;
}
else if(t != c){
remo(u, c);
remo(c, u);
adj[u].pb(t);
adj[v].pb(t);
adj[c].pb(t);
adj[t].pb(u);
adj[t].pb(c);
adj[t].pb(v);
mark[t] = true;
return;
}
}
//cout << "ok " << sub << endl;
if(sub != -1){
rem[c] = true;
add(sub, v);
return;
}
adj[c].pb(v);
adj[v].pb(c);
}
void Solve(int nn){
n = nn;
for(int i = 0; i < n; i++){
per[i] = i;
}
shuffle(per, per + n, rng);
for(int i = 0; i < n; i++){
rev[per[i]] = i;
//cout << i << ' ' << per[i] << endl;
}
for(int i = 1; i < n; i++) if(!mark[i]){
fill(rem, rem + n + 5, false);
lev = 0;
add(0, i);
mark[i] = true;
}
for(int i = 0; i < n; i++) for(auto u : adj[i]){
//cout << "edge " << i << ' '<< u << ' ' << per[i] << ' ' << per[u] << endl;
if(per[i] < per[u]) Bridge(per[i], per[u]);
}
return;
}
/*
4
0 3
2 3
1 3
*/
