// Query Bridge
#include "meetings.h"
#include <bits/stdc++.h>
using namespace std;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const int maxn = 2e3 + 5;
using ii = pair<int, int>;
int n;
set<ii> ans;
map<int, map<int, map<int, int>>> mem;
int ask(int u, int v, int w) {
{
int mn = min({u, v, w});
int mx = max({u, v, w});
int md = u + v + w - mn - mx;
u = mn, v = md, w = mx;
}
if(u == v or v == w) return v;
if(mem[u][v].find(w) == mem[u][v].end()) return mem[u][v][w] = Query(u, v, w);
else return mem[u][v][w];
}
void add_edge(int u, int v) {
if(u > v) swap(u, v);
// cout << "addded = " << u << ' ' << v << endl;
ans.insert(ii(u, v));
}
void solve(vector<int> &s) {
if(s.size() < 2) return;
if(s.size() == 2) {
add_edge(s[0], s[1]);
return;
}
shuffle(s.begin(), s.end(), rng);
set<int> path_nodes;
map<int, int> mp;
int p = s[0], q = s[1];
for(int u : s) {
mp[u] = ask(p, q, u);
path_nodes.insert(mp[u]);
}
path_nodes.erase(p);
path_nodes.erase(q);
vector<int> path(path_nodes.begin(), path_nodes.end());
shuffle(path.begin(), path.end(), rng);
sort(path.begin(), path.end(), [&](int u, int v){ return ask(p, u, v) == u; });
for(int i = 1; i < path.size(); i++) {
add_edge(path[i - 1], path[i]);
}
if(path.size()) {
add_edge(path[0], p);
add_edge(path.back(), q);
} else add_edge(p, q);
map<int, vector<int>> to;
for(auto i : mp) {
to[i.second].emplace_back(i.first);
}
for(auto i : to) {
solve(i.second);
}
}
void Solve(int N) {
vector<int> v(N);
iota(v.begin(), v.end(), 0);
solve(v);
for(ii i : ans) Bridge(i.first, i.second);
}
