#include "meetings.h"
#include<bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using vi = vector<int>;
using vl = vector<ll>;
using vb = vector<bool>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using ld = long double;
using str = string;
#define all(a) a.begin(), a.end()
#define print(a) for (auto elem:a) cout<<elem<<' '; cout<<'\n'
#define segprep(b) resize(1<<((int)ceil(log2(b.size()))+1))
#define FOR(a) for (int _ = 0; _ < a; _++)
const int SEED = 1;
void srt(int &a, int &b, int &c){
    vi tmp = {a, b, c};
    sort(all(tmp));
    a = tmp.front();
    b = tmp.at(1);
    c = tmp.back();
}
int randint(const int l, const int r){
    int res = rand()%(r-l)+l;
    assert(l <= res && res < r);
    return res;
}
struct query{
    int u, v, w;
};
bool operator<(const query &a, const query&b){
    return (vi{a.u, a.v, a.w} < vi{b.u, b.v, b.w});
}
map<query, int> asked;
int ask_query(int u, int v, int w){
    srt(u, v, w);
    query quest{u, v, w};
    if (asked.find(quest) != asked.end()){
        return asked.at(quest);
    }
    int ans = Query(u, v, w);
    asked.insert({quest, ans});
    return ans;
    // return Query(u, v, w);
}
int n;
vector<vi> graph;
void solve_set(vi verts){
    // print(verts);
    if (verts.size() == 1) return;
    if (verts.size() == 2){
        int first = verts.front(), second = verts.back();
        if (first > second) swap(first, second);
        Bridge(first, second);
        graph.at(first).push_back(second);
        graph.at(second).push_back(first);
        return;
    }
    int root_ind = randint(0, (int)verts.size());
    int root = verts.at(root_ind);
    verts.erase(verts.begin()+root_ind);
    int second_ind = randint(0, (int)verts.size());
    int second = verts.at(second_ind);
    verts.erase(verts.begin()+second_ind);
    // test roota
    int a = 0, c = 0, b = 0, ans, sz = verts.size();
    for (int i = 0; i < sz; i++){
        ans = ask_query(root, second, verts.at(i));
        if (ans == root){
            c++;
        }
        else if (ans == second){
            a++;
        }
        else{
            b++;
        }
    }
    if (abs(2*a-sz) < abs(2*c-sz)) swap(root, second);
    vi subtr = {second};
    vi left_nodes = {root};
    vb in_path_to_second(n, false);
    int vert;
    for (int i = 0; i < sz; i++){
        vert = verts.at(i);
        ans = ask_query(root, second, vert);
        if (ans == root){
            left_nodes.push_back(vert);
            continue;
        }
        subtr.push_back(vert);
        if (ans == vert){
            in_path_to_second.at(vert) = true;
        }
        // if (i == 5 && subtr.size() == 1){
        //     // slaby second, rerun
        //     second_ind = randint(0, (int)verts.size()-1);
        //     if (second_ind >= root_ind) second_ind++;
        //     second = verts.at(second_ind);
        //     subtr = {second};
        //     left_nodes = {root};
        //     fill(all(in_path_to_second), false);
        //     i = -1;
        // }
    }
    solve_set(subtr);
    solve_set(left_nodes);
    // znalezc polaczenie
    vert = second;
    int parent = second;
    bool moved;
    // cout<<"przed petla: ";
    // print(verts);
    do{
        // cout<<"hi\n";
        moved = false;
        for (const auto &son:graph.at(vert)){
            if (son != parent && in_path_to_second.at(son)){
                parent = vert;
                vert = son;
                moved = true;
                break;
            }
        }
    } while(moved);
    if (vert > root) swap(vert, root);
    Bridge(vert, root);
    graph.at(vert).push_back(root);
    graph.at(root).push_back(vert);
}
void Solve(int N){
    n = N;
    srand(SEED);
    graph.resize(n);
    vi nodes(n);
    for (int i = 0; i < n; i++) nodes.at(i) = i;
    shuffle(all(nodes), mt19937(SEED));
    solve_set(nodes);
}
/*
const int MAX_N = 2000;
const int MAX_CALLS = 100000;
void WrongAnswer(int code) {
    printf("Wrong Answer [%d]\n", code);
    exit(0);
}
int N, num_calls;
std::vector<int> graph_[MAX_N];
std::set<std::pair<int, int>> edges, edges_reported;
int weight[MAX_N];
bool Visit(int p, int e, int rt = -1) {
    if (p == e) {
    ++weight[p];
    return true;
    }
    for (int q : graph_[p]) {
    if (q != rt) {
        if (Visit(q, e, p)) {
        ++weight[p];
        return true;
        }
    }
    }
    return false;
}
int Query(int u, int v, int w) {
    if (!(0 <= u && u <= N - 1 && 0 <= v && v <= N - 1 && 0 <= w && w <= N - 1 &&
        u != v && u != w && v != w)) {
        WrongAnswer(1);
    }
    if (++num_calls > MAX_CALLS) {
        WrongAnswer(2);
    }
    std::fill(weight, weight + N, 0);
    Visit(u, v);
    Visit(u, w);
    Visit(v, w);
    for (int x = 0; x < N; ++x) {
        if (weight[x] == 3) {
            return x;
        }
    }
    printf("Error: the input may be invalid\n");
    exit(0);
}
void Bridge(int u, int v) {
    if (!(0 <= u && u < v && v <= N - 1)) {
        printf("u: %d, v: %d\n", u, v);
        WrongAnswer(3);
    }
    if (!(edges.count(std::make_pair(u, v)) >= 1)) {
        WrongAnswer(4);
    }
    if (!(edges_reported.count(std::make_pair(u, v)) == 0)) {
        WrongAnswer(5);
    }
    edges_reported.insert(std::make_pair(u, v));
}
int main() {
    if (scanf("%d", &N) != 1) {
        fprintf(stderr, "Error while reading input\n");
        exit(1);
    }
    for (int i = 0; i < N - 1; ++i) {
        int u, v;
        if (scanf("%d%d", &u, &v) != 2) {
            fprintf(stderr, "Error while reading input\n");
            exit(1);
        }
        graph_[u].push_back(v);
        graph_[v].push_back(u);
        edges.insert(std::make_pair(u, v));
    }
    num_calls = 0;
    Solve(N);
    if (edges_reported.size() != static_cast<size_t>(N - 1)) {
        WrongAnswer(6);
    }
    printf("Accepted: %d\n", num_calls);
    return 0;
}
*/
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