#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")
#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/rope>
#include "meetings.h"
using namespace std;
using namespace __gnu_pbds;
using namespace __gnu_cxx;
random_device(rd);
mt19937 rng(rd());
const long long FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
struct custom_hash
{
template<class T>
unsigned long long operator()(T v) const
{
unsigned long long x = v;
x += FIXED_RANDOM;
// x += 11400714819323198485ull;
// x = (x ^ (x >> 30)) * 13787848793156543929ull;
x = (x ^ (x >> 27)) * 10723151780598845931ull;
return x ^ (x >> 31);
}
};
template<class T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<class T, class U> using hash_table = gp_hash_table<T, U, custom_hash>;
template<class T>
T randomize(T mod)
{
return (uniform_int_distribution<T>(0, mod - 1))(rng);
}
template<class T>
void readi(T &x)
{
x = 0;
bool negative = false;
char c = ' ';
while (c < '-')
{
c = getchar();
}
if (c == '-')
{
negative = true;
c = getchar();
}
while (c >= '0')
{
x = x * 10 + (c - '0');
c = getchar();
}
if (negative)
{
x = -x;
}
}
template<class T>
void printi(T output)
{
if (output == 0)
{
putchar('0');
return;
}
if (output < 0)
{
putchar('-');
output = -output;
}
int buf[20], n = 0;
while(output)
{
buf[n] = ((output % 10));
output /= 10;
n++;
}
for (n--; n >= 0; n--)
{
putchar(buf[n] + '0');
}
return;
}
template<class T>
void ckmin(T &a, T b)
{
a = min(a, b);
}
template<class T>
void ckmax(T &a, T b)
{
a = max(a, b);
}
long long expo(long long a, long long e, long long mod)
{
return ((e == 0) ? 1 : ((expo(a * a % mod, e >> 1, mod)) * ((e & 1) ? a : 1) % mod));
}
template<class T, class U>
void nmod(T &x, U mod)
{
if (x >= mod) x -= mod;
}
template<class T>
T gcd(T a, T b)
{
return (b ? gcd(b, a % b) : a);
}
#define y0 ___y0
#define y1 ___y1
#define MP make_pair
#define PB push_back
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define DBG(x) cerr << #x << " = " << (x) << endl
#define SZ(x) ((int) ((x).size()))
#define FOR(i, a, b) for (auto i = (a); i < (b); i++)
#define FORD(i, a, b) for (auto i = (a) - 1; i >= (b); i--)
#define ALL(x) (x).begin(), (x).end()
const long double PI = 4.0 * atan(1.0);
const long double EPS = 1e-9;
#define MAGIC 347
#define SINF 10007
#define CO 1000007
#define INF 1000000007
#define BIG 1000000931
#define LARGE 1696969696967ll
#define GIANT 2564008813937411ll
#define LLINF 2696969696969696969ll
#define MAXN 2013
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<ld, ld> pdd;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<ld> vd;
typedef vector<pii> vpi;
typedef vector<pll> vpl;
typedef vector<pdd> vpd;
int N;
int S, T;
hash_table<int, int> res[MAXN];
vpi ans;
int queries = 0;
int ask(int a, int b, int c)
{
queries++;
assert(queries <= 100000);
if (a > b) swap(a, b);
if (b > c) swap(b, c);
if (a > b) swap(a, b);
if (res[a].find(b * N + c) != res[a].end())
{
return res[a][b * N + c];
}
int ret = Query(a, b, c);
res[a][b * N + c] = ret;
return ret;
}
bool cmp(int a, int b)
{
return (ask(S, a, b) == a);
}
void solve(vi vec)
{
if (SZ(vec) <= 1) return;
FOR(i, 1, SZ(vec))
{
swap(vec[i], vec[randomize(i + 1)]);
}
// for (int v : vec)
// {
// DBG(v);
// }
// cerr << "yes\n";
S = vec.back(); vec.pop_back();
T = vec.back(); vec.pop_back();
vi path;
map<int, vi> mp;
mp[S].PB(S); mp[T].PB(T);
for (int u : vec)
{
int w = ask(S, u, T);
if (w == u) path.PB(u);
mp[w].PB(u);
}
if (!path.empty())
{
sort(ALL(path), cmp);
ans.PB({S, path[0]});
FOR(i, 0, SZ(path) - 1)
{
ans.PB({path[i], path[i + 1]});
}
ans.PB({path.back(), T});
}
else
{
ans.PB({S, T});
}
for (auto p : mp)
{
solve(p.se);
}
}
void Solve(int n)
{
N = n;
if (N == 1)
{
return;
}
//everything has degree at most 18!
//you want n * max
//how can you find everybody that's connected to 0?
vi lol;
FOR(i, 0, N)
{
lol.PB(i);
}
solve(lol);
for (pii p : ans)
{
if (p.fi > p.se) swap(p.fi, p.se);
// cerr << "ye " << p.fi << ' ' << p.se << endl;
Bridge(p.fi, p.se);
}
}
