#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 {
if (sub == 4) {
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();
kids[adj[i]].push_back(i);
++cnt[adj[i]];
}
}
for (int i = 0; i < m; ++i) {
if (max(mega[i], dist[b] - mega[i]) == ans) {
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];
}
if (max({L, R, cnt[i]}) <= n / 2) {
return ans;
}
}
}
return -ans;
} else {
vector dist(n, vector<int>(n));
for (int i = 0; i < n; ++i) {
for (int j = i + 1; j < n; ++j) {
dist[i][j] = dist[j][i] = getDistance(i, j);
}
}
vector mp(n, vector<map<int, int>>(n));
vector<int> verts = {228};
vector<vector<pair<int, int>>> kids = {{}};
for (int i = 0; i < n; ++i) {
for (int j = i + 1; j < n; ++j) {
for (int k = j + 1; k < n; ++k) {
int a = dist[i][j];
int b = dist[j][k];
int c = dist[k][i];
int x = (a - b + c) / 2;
int y = a - x;
int z = c - x;
int s = max({mp[i][j][x], mp[j][k][y], mp[i][k][x]});
if (s == 0) {
s = verts.size();
verts.push_back(0);
kids.emplace_back();
}
kids[s].emplace_back(x, i);
kids[s].emplace_back(y, j);
kids[s].emplace_back(z, k);
mp[i][j][x] = mp[j][k][y] = mp[i][k][x] = s;
verts[s] = max({verts[s], x, y, z});
}
}
}
int ans = *min_element(verts.begin() + 1, verts.end());
for (int r = 1; r < kids.size(); ++r) {
if (verts[r] == ans) {
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];
}
};
sort(kids[r].begin(), kids[r].end());
kids[r].resize(unique(kids[r].begin(), kids[r].end()) - kids[r].begin());
assert(kids[r].size() == n);
for (int i = 0; i < n; ++i) {
for (int j = 0; j < n; ++j) {
if (i != j) {
auto [wx, x] = kids[r][i];
auto [wy, y] = kids[r][j];
assert(wx + wy >= dist[x][y]);
if (wx + wy != dist[x][y]) {
unite(x, y);
}
}
}
}
if (*max_element(sz.begin(), sz.end()) <= n / 2) {
return ans;
}
}
}
return -ans;
}
}
}
