// In the name of Allah
#include <bits/stdc++.h>
#include "towns.h"
using namespace std;
typedef long long int ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef complex<ld> cld;
#define all(x) (x).begin(),(x).end()
#define len(x) ((ll) (x).size())
#define F first
#define S second
#define pb push_back
#define sep ' '
#define endl '\n'
#define Mp make_pair
#define kill(x) cout << x << '\n', exit(0)
#define set_dec(x) cout << fixed << setprecision(x);
#define file_io(x,y) freopen(x, "r", stdin); freopen(y, "w", stdout);
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int n;
int v1, v2, u1, u2;
const int maxn = 110 + 4;
ll dis[maxn][maxn], R;
int p[maxn], sz[maxn];
int get(int a) {
return (p[a] == a) ? a : p[a] = get(p[a]);
}
void merge(int a, int b) {
a = get(a); b = get(b);
if (a == b) return ;
if (sz[a] > sz[b]) swap(a, b);
p[a] = b; sz[b] += sz[a]; sz[a] = 0;
}
ll get_dis(int u, int v) {
if (dis[u][v] == -1) {
dis[u][v] = dis[v][u] = getDistance(u, v);
}
return dis[u][v];
}
bool ok(ll R) {
bool flag = 0;
ll dx = get_dis(v1, v2);
for (int i = 0; i < n; i++) {
ll d1 = get_dis(v1, i), d2 = get_dis(v2, i);
ll x = (d1 + d2 - dx) / 2;
if (d2 - x == R) {
flag = 1;
break;
}
}
if (!flag) return 0;
int t1 = 0, t2 = 0;
for (int i = 0; i < n; i++) {
ll d1 = get_dis(v1, i), d2 = get_dis(v2, i);
ll x = (d1 + d2 - dx) / 2;
if (d2 - x < R) t1++;
else if (d2 - x > R) t2++;
}
return (max(t1, t2) * 2 <= n);
}
void check(int i, int j) {
ll dx = get_dis(v1, v2);
ll d1 = get_dis(v1, i), d2 = get_dis(v2, i);
ll x1 = (d1 + d2 - dx) / 2;
d1 = get_dis(v1, j), d2 = get_dis(v2, j);
ll x2 = (d1 + d2 - dx) / 2;
ll valx = (x1 + x2 - get_dis(i, j)) / 2;
if (valx > 0) merge(i, j);
return ;
}
int hubDistance(int N, int sub) {
n = N;
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (i == j) dis[i][j] = 0;
else dis[i][j] = -1;
}
}
v1 = 0, u1 = v1;
for (int i = 0; i < n; i++) {
if (get_dis(v1, i) > get_dis(v1, u1)) u1 = i;
}
v2 = u1, u2 = v2;
for (int i = 0; i < n; i++) {
if (get_dis(v2, i) > get_dis(v2, u2)) u2 = i;
}
ll dx = get_dis(v1, v2);
ll D = get_dis(u1, u2); R = D;
for (int i = 0; i < n; i++) {
ll d1 = get_dis(v1, i), d2 = get_dis(v2, i);
ll x = (d1 + d2 - dx) / 2;
R = min(R, max(d2 - x, D - (d2 - x)));
}
if (!ok(R) && !ok(D - R)) return -R;
iota(p, p + n, 0); fill(sz, sz + n, 1);
int v = 0, cnt = 1;
for (int i = 1; i < n; i++) {
if (cnt == 0) {
v = i; cnt = 1;
}
else {
check(i, v);
if (get(i) == get(v)) cnt++;
else cnt--;
}
}
v = get(v);
for (int i = 0; i < n; i++) {
if (get(i) != i || get(i) == v) continue;
check(i, v);
}
if (sz[v] * 2 <= n) return R;
else return -R;
}
