#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define pb emplace_back
#define AI(i) begin(i), end(i)
template<class T> bool chmin(T &a, T b) { return b < a && (a = b, true); }
template<class T> bool chmax(T &a, T b) { return a < b && (a = b, true); }
#ifdef KEV
#define DE(args...) kout("[ " + string(#args) + " ] = ", args)
void kout() { cerr << endl; }
template<class T, class ...U> void kout(T a, U ...b) { cerr << a << ' ', kout(b...); }
template<class T> void debug(T l, T r) { while (l != r) cerr << *l << " \n"[next(l)==r], ++l; }
#else
#define DE(...) 0
#define debug(...) 0
#endif
const int MAX_N = 200;
#include "towns.h"
int mem_dis[MAX_N][MAX_N], n, h[MAX_N];
int dis(int a, int b) {
if (mem_dis[a][b] || a == b) return mem_dis[a][b];
return mem_dis[a][b] = mem_dis[b][a] = getDistance(a, b);
}
int get_far(int x) {
int d = 0, g = -1;
for (int i = 0;i < n;++i) if (i != x)
if (chmax(d, dis(x, i)))
g = i;
return g;
}
bool too_big(int x) { return x > n / 2; }
int hubDistance(int N, int sub) {
memset(mem_dis, 0, sizeof(mem_dis));
n = N;
int f = get_far(0), g = get_far(f);
map<int, vector<int>> cnt;
for (int i = 0;i < n;++i) {
int y = dis(f, i), z = dis(g, i), x = dis(f, g);
h[i] = (y + z - x) / 2;
//++cnt[y - h[i]];
cnt[y - h[i]].pb(i);
}
int ret = dis(f, g);
for (auto [a, _] : cnt)
chmin(ret, max(a, dis(f, g) - a));
auto valid = [&](vector<int> child) {
while (child.size()) {
if (!too_big(child.size())) return true;
vector<int> a {child[0]}, b;
for (int i = 1;i < child.size();++i) {
int x = a[0], y = child[i];
if (dis(x, y) == h[x] + h[y])
b.pb(y);
else
a.pb(y);
}
if (too_big(a.size())) return false;
child = b;
}
return true;
};
bool has_hub = false;
for (auto [a, child] : cnt)
if (max(a, dis(f, g) - a) == ret) {
int l = 0, r = 0;
for (auto [w, c] : cnt) {
if (w < a) l += c.size();
if (w > a) r += c.size();
}
if (too_big(max(l, r))) continue;
if (valid(child)) {
has_hub = true;
break;
}
}
if (!has_hub) ret *= -1;
return ret;
}
