#include <bits/stdc++.h>
#define mp make_pair
#define pb push_back
#define X first
#define Y second
#define y0 y12
#define y1 y22
#define INF 987654321
#define PI 3.141592653589793238462643383279502884
#define fup(i, a, b, c) for (int(i) = (a); (i) <= (b); (i) += (c))
#define fdn(i, a, b, c) for (int(i) = (a); (i) >= (b); (i) -= (c))
#define MEM0(a) memset((a), 0, sizeof(a));
#define MEM_1(a) memset((a), -1, sizeof(a));
#define ALL(a) a.begin(), a.end()
#define SYNC \
ios_base::sync_with_stdio(false); \
cin.tie(0)
using namespace std;
typedef long long ll;
typedef long double ld;
typedef double db;
typedef unsigned int uint;
typedef unsigned long long ull;
typedef pair<int, int> Pi;
typedef pair<ll, ll> Pll;
typedef pair<ld, ld> Pd;
typedef vector<int> Vi;
typedef vector<ll> Vll;
typedef vector<ld> Vd;
typedef vector<Pi> VPi;
typedef vector<Pll> VPll;
typedef vector<Pd> VPd;
typedef tuple<int, int, int> iii;
typedef tuple<int, int, int, int> iiii;
typedef tuple<ll, ll, ll> LLL;
typedef vector<iii> Viii;
typedef vector<LLL> VLLL;
typedef complex<double> base;
const int MOD = 1000000007;
ll POW(ll a, ll b, ll MMM = MOD) {
ll ret = 1;
for (; b; b >>= 1, a = (a * a) % MMM)
if (b & 1)
ret = (ret * a) % MMM;
return ret;
}
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
ll lcm(ll a, ll b) {
if (a == 0 || b == 0)
return a + b;
return a * (b / gcd(a, b));
}
int dx[] = { 0, 1, 0, -1, 1, 1, -1, -1 }, dy[] = { 1, 0, -1, 0, 1, -1, 1, -1 };
int ddx[] = { -1, -2, 1, -2, 2, -1, 2, 1 }, ddy[] = { -2, -1, -2, 1, -1, 2, 1, 2 };
#include "meetings.h"
#define kill kool
Vi v[2005];
void discon(int x, int y) {
for (int &z : v[x]) {
if (z == y) {
z = v[x].back();
v[x].back() = y;
break;
}
}
for (int &z : v[y]) {
if (z == x) {
z = v[y].back();
v[y].back() = x;
break;
}
}
v[x].pop_back();
v[y].pop_back();
}
void con(int x, int y) {
v[x].pb(y);
v[y].pb(x);
}
bool chk[2005], kill[2005];
int sz[2005];
int getSz(int N, int pp) {
sz[N] = 1;
for (int next : v[N]) {
if (next == pp || kill[next])
continue;
sz[N] += getSz(next, N);
}
return sz[N];
}
int get_centroid(int N, int pp, int cap) {
for (int next : v[N]) {
if (kill[next] || next == pp)
continue;
if (sz[next] > cap)
return get_centroid(next, N, cap);
}
return N;
}
void Solve(int N) {
chk[0] = chk[1] = chk[2] = 1;
int w = Query(0, 1, 2);
if (w > 2) {
chk[w] = 1;
con(0, w);
con(1, w);
con(2, w);
} else {
fup(i, 0, 2, 1) if (w != i) con(i, w);
}
fup(i, 3, N - 1, 1) {
MEM0(kill);
if (chk[i])
continue;
chk[i] = 1;
int pr = 0;
while (1) {
int cap = getSz(pr, -1);
int R = get_centroid(pr, -1, cap / 2);
getSz(R, -1);
sort(ALL(v[R]), [&](int a, int b) { return sz[a] > sz[b]; });
kill[R] = 1;
int t = -1;
fup(j, 1, (int)v[R].size() - 1, 2) {
int a = v[R][j - 1], b = v[R][j];
int x = Query(a, i, b);
if (x == i) {
int T = Query(R, i, a);
if (T == i) {
discon(R, a);
con(R, i);
con(i, a);
} else {
discon(R, b);
con(R, i);
con(i, b);
}
goto FIN;
} else if (x != R) {
t = x;
break;
}
}
if (t == -1 && v[R].size() & 1) {
int x = Query(R, i, v[R].back());
if (x == i) {
int B = v[R].back();
discon(R, B);
con(R, i);
con(i, B);
goto FIN;
} else if (x != R)
t = x;
}
if (t == -1) {
con(R, i);
goto FIN;
} else {
pr = t;
}
}
FIN:;
}
fup(i, 0, N - 1, 1) {
for (int x : v[i]) {
if (x > i)
Bridge(i, x);
}
}
}
