#include <bits/stdc++.h>
#include "towns.h"
using namespace std;
int hubDistance(int n, int sub) {
map<pair<int, int>, int> mp;
auto mygetDistance = [&](int x, int y) {
if (mp.count({x, y})) {
return mp[{x, y}];
} else {
return mp[{x, y}] = mp[{y, x}] = getDistance(x, y);
}
};
if (sub <= 2) {
vector<int> dist(n);
for (int i = 0; i < n; ++i) {
dist[i] = mygetDistance(i, 0);
}
int v = max_element(dist.begin(), dist.end()) - dist.begin();
for (int i = 0; i < n; ++i) {
dist[i] = mygetDistance(i, v);
}
int u = max_element(dist.begin(), dist.end()) - dist.begin();
vector<int> dist2(n);
for (int i = 0; i < n; ++i) {
dist2[i] = mygetDistance(i, u);
}
int ans = numeric_limits<int>::max();
for (int i = 0; i < n; ++i) {
int e = dist[i] + dist2[i] - dist[u] >> 1;
ans = min(ans, max(dist[i] - e, dist2[i] - e));
}
return ans;
} else {
vector<int> dist(n), e(n);
for (int i = 0; i < n; ++i) {
dist[i] = mygetDistance(i, 0);
}
int a = max_element(dist.begin(), dist.end()) - dist.begin();
for (int i = 0; i < n; ++i) {
dist[i] = mygetDistance(i, a);
}
int b = max_element(dist.begin(), dist.end()) - dist.begin();
vector<int> dist2(n);
for (int i = 0; i < n; ++i) {
dist2[i] = mygetDistance(i, b);
}
int ans = numeric_limits<int>::max();
vector<int> mega;
for (int i = 0; i < n; ++i) {
if (i != b && i != a) {
e[i] = (dist[i] + dist2[i] - dist[b]) >> 1;
mega.push_back(dist[i] - e[i]);
ans = min(ans, max(mega.back(), dist[b] - mega.back()));
}
}
sort(mega.begin(), mega.end());
mega.resize(unique(mega.begin(), mega.end()) - mega.begin());
const int m = mega.size();
vector<int> adj(n), cnt(m);
vector<vector<int>> kids(m);
for (int i = 0; i < n; ++i) {
if (i != b && i != a) {
adj[i] = lower_bound(mega.begin(), mega.end(), dist[i] - e[i]) - mega.begin();
assert(mega[adj[i]] + e[i] == dist[i]);
kids[adj[i]].push_back(i);
++cnt[adj[i]];
}
}
int vis = 0;
for (int i = 0; i < m; ++i) {
if (max(mega[i], dist[b] - mega[i]) == ans) {
++vis;
int L = 1, R = 1;
for (int j = 0; j < i; ++j) {
L += cnt[j];
}
for (int j = i + 1; j < m; ++j) {
R += cnt[j];
}
vector<int> p(n), sz(n, 1);
iota(p.begin(), p.end(), 0);
auto get = [&](int x) {
while (x != p[x]) x = p[x] = p[p[x]];
return x;
};
auto unite = [&](int x, int y) {
x = get(x), y = get(y);
if (x != y) {
p[y] = x;
sz[x] += sz[y];
}
};
for (int x : kids[i]) {
for (int y : kids[i]) {
if (x != y) {
if (e[x] + e[y] > mygetDistance(x, y)) {
unite(x, y);
}
}
}
}
int mx = *max_element(sz.begin(), sz.end());
if (max({L, R, mx}) <= n / 2) {
return -ans;
}
}
}
return ans;
}
}
