#include "towns.h"
#include <bits/stdc++.h>
#include <random>
#include <utility>
using namespace std;
#ifndef LOCAL
#define cerr if(false) cerr
#endif
template<class T, class T2>
inline bool chkmax(T &a, const T2 &b) { return a < b ? a = b, true : false; }
template<class T, class T2>
inline bool chkmin(T &a, const T2 &b) { return a > b ? a = b, true : false; }
typedef long long ll;
const int MAX_N = 128;
const ll inf = 1e18;
int n;
map<pair<int,int>, ll> q;
ll makeQuery(int a, int b) {
if(a > b) swap(a, b);
if(a == b) return 0;
pair<int,int> key = {a, b};
if(q.find(key) == q.end())
q[key] = getDistance(a, b);
return q[key];
}
struct DSU {
int parent[MAX_N], sz[MAX_N];
void init() {
for (int i = 0; i < n; i++) {
parent[i] = i;
sz[i] = 1;
}
}
int find(int a) {
return parent[a] == a ? a : parent[a] = find(parent[a]);
}
void unite(int a, int b) {
a = find(a); b = find(b);
if(a == b) return;
if(sz[a] > sz[b]) swap(a, b);
parent[a] = b;
sz[b] += sz[a];
}
};
int hubDistance(int N, int sub) {
q.clear();
n = N;
vector<ll> to0(n, 0), tor1(n, 0);
for (int i = 1; i < n; i++) {
to0[i] = makeQuery(0, i);
}
ll maxd = 0;
int pos = 0;
for (int i = 0; i < n; i++) {
if(chkmax(maxd, to0[i])) {
pos = i;
}
}
int r1 = pos;
for (int i = 0; i < n; i++) {
tor1[i] = makeQuery(r1, i);
}
maxd = 0;
pos = 0;
for (int i = 0; i < n; i++) {
if(chkmax(maxd, tor1[i])) {
pos = i;
}
}
int r2 = pos;
vector<pair<ll,ll>> vc(n);
for (int i = 0; i < n; i++) {
ll dis = (to0[r1] + tor1[i] - to0[i]) / 2;
vc[i] = {dis, tor1[i] - dis}; // first: hub candidate distance, second: remaining distance
}
ll ans = maxd;
for (int i = 0; i < n; i++) {
ans = min(ans, max(vc[i].first, tor1[r2] - vc[i].first));
}
vector<ll> want;
for (int i = 0; i < n; i++) {
if(ans == max(vc[i].first, tor1[r2] - vc[i].first))
want.push_back(vc[i].first);
}
int ok = 0;
DSU dsu;
for (auto dis : want) {
int s = 0, m = 0, l = 0;
vector<int> now;
for (int i = 0; i < n; i++) {
if(vc[i].first < dis)
s++;
else if(vc[i].first == dis)
now.push_back(i);
else
l++;
}
if(s > n / 2 || l > n / 2) continue;
int nx = now[0], mis = 1, OK = 1;
dsu.init();
for (size_t i = 1; i < now.size(); i++) {
int x = now[i];
if(nx == 0) {
mis = 1;
nx = now[i];
continue;
}
if(makeQuery(nx, x) < vc[nx].second + vc[x].second) {
dsu.unite(nx, x);
mis++;
} else {
mis--;
}
if(mis == 0) nx = 0;
}
for (size_t i = 0; i < now.size(); i++) {
int x = now[i];
if(x == dsu.find(x)) {
if(makeQuery(nx, x) < vc[nx].second + vc[x].second)
dsu.unite(nx, x);
}
}
for (size_t i = 0; i < now.size(); i++) {
int x = now[i];
if(x == dsu.find(x) && dsu.sz[x] > n / 2)
OK = 0;
}
ok |= OK;
}
return (ok == 1 ? ans : -ans);
}
