#include "towns.h"
#include <bits/stdc++.h>
using namespace std;
const int maxn = 120;
const int maxm = 1e6+10;
const int inf = 0x3f3f3f3f;
int qs[maxn][maxn];
int sol[maxm];
vector<int> v;
vector<int> li, buk;
int query(int a, int b) {
if (a > b) swap(a, b);
if (qs[a][b] == -1) qs[a][b] = getDistance(a, b);
return qs[a][b];
}
int a, b;
int B;
bool subtree(int x, int y) {
int xd = (query(a, x) + query(b, x) - query(a, b)) / 2;
int yd = (query(a, y) + query(b, y) - query(a, b)) / 2;
return xd + yd - query(x, y) > 0;
}
int hubDistance(int n, int sub) {
memset(qs, -1, sizeof qs);
memset(sol, inf, sizeof sol);
for (int i = 0; i < n; i++)
qs[i][i] = 0;
a = 0, b = 0;
for (int i = 0; i < n; i++)
if (query(0, a) < query(0, i)) a = i;
for (int i = 0; i < n; i++)
if (query(a, b) < query(a, i)) b = i;
B = b; b = 0;
for (int i = 0; i < n; i++) {
int cd = (query(a, i) + query(b, i) - query(a, b)) / 2;
int ad = query(a, i) - cd;
int bd = query(a, B) - ad;
sol[ad] = max({cd, ad, bd});
}
int hu = 0;
for (int i = 0; i < maxm; i++)
if (sol[hu] > sol[i]) hu = i;
int lef = 0, rig = 0;
v.clear();
for (int i = 0; i < n; i++) {
int cd = (query(a, i) + query(b, i) - query(a, b)) / 2;
int ad = query(a, i) - cd;
if (ad < hu) lef++;
else if (ad > hu) rig++;
else v.push_back(i);
}
li.clear();
buk.clear();
li.push_back(v[0]);
for (int i = 1; i < n; i++) {
if (subtree(v[i], li.back())) buk.push_back(v[i]);
else {
li.push_back(v[i]);
if (!buk.empty()) {
li.push_back(buk.back());
buk.pop_back();
}
}
}
int cnt = buk.size();
for (int i = 0; i < li.size(); i++)
if (subtree(li[i], li.back())) cnt++, i++;
if (max({cnt, lef, rig}) > n / 2) return -sol[hu];
else return sol[hu];
}
