#include "meetings.h"
#include <bits/stdc++.h>
using namespace std;
using vi = vector<int>;
map<tuple<int, int, int>, int> Bfq;
int query(int a, int b, int c) {
if(a > b) return query(b, a, c);
if(a > c) return query(c, b, a);
if(b > c) return query(a, c, b);
if(Bfq.count({a, b, c})) return Bfq[{a, b, c}];
int v = Query(a, b, c);
Bfq[{a, b, c}] = v;
return v;
}
#define pb push_back
void bridge(int a, int b) {
Bridge(min(a, b), max(a, b));
}
void solve(int root, const vi& U, mt19937 rng) {
if(U.empty()) return;
map<int, vi> Altii;
vi lant;
int pivot = U[uniform_int_distribution<int>(0, U.size() - 1)(rng)];
lant.pb(pivot);
for(auto it : U) {
if(it == pivot) continue;
int v = query(root, it, pivot);
if(v == it) lant.pb(v);
else Altii[v].pb(it);
}
sort(lant.begin(), lant.end(), [&](auto a, auto b) {
return query(root, a, b) == a;
});
bridge(root, lant[0]);
for(int i = 0; i < lant.size() - 1; ++i)
bridge(lant[i], lant[i+1]);
for(auto &[rn, Un] : Altii)
solve(rn, Un, rng);
}
void Solve(int N) {
Bfq.clear();
mt19937 rng(2);
vi E;
for(int i = 1; i < N; ++i) E.pb(i);
solve(0, E, rng);
}
