#include "towns.h"
#include <bits/stdc++.h>
using namespace std;
int hubDistance(int N, int sub) {
vector<vector<int>> D(N, vector<int>(N, 0));
for(int i=1;i<N;i++) D[0][i] = D[i][0] = getDistance(0, i);
int E = max_element(D[0].begin(), D[0].end()) - D[0].begin();
for(int i=0;i<N;i++) if(i != E) D[E][i] = D[i][E] = getDistance(E, i);
int X = max_element(D[E].begin(), D[E].end()) - D[E].begin();
vector<int> C(N, 0), mp(1001001, 0);
for(int i=0;i<N;i++) mp[C[i] = (D[E][i]+D[0][E] - D[0][i])/2]++;
int R = 1e9, h1 = -1, h2 = -1;
for(int i=0;i<N;i++) if(i != E && C[i] <= C[X]) {
auto r = max(C[i], D[E][X]-C[i]);
if(R > r) R = r, h1 = i, h2 = -1;
else if(R == r && C[h1] != C[i]) h2 = i;
}
if(sub <= 2) return R;
if(h2 != -1 && C[h1] > C[h2]) swap(h1, h2);
vector<int> c(2, 0);
for(int i=0;i<N;i++) c[C[i] > C[h1]]++;
if(h2 != -1) {
if(max(c[0], c[1]) <= N/2) return R;
if(c[0] <= N/2) h1 = h2, c[0] += mp[C[h2]], c[1] -= mp[C[h2]];
}
c[0] -= mp[C[h1]];
if(max(c[0], c[1]) > N/2) return -R;
vector<int> v;
for(int i=0;i<N;i++) if(C[i] == C[h1]) v.push_back(i);
vector<vector<int>> same(N, vector<int>(N, -1));
auto check = [&](int x, int y) {
if(x == y) return 1;
if(same[x][y] != -1) return same[x][y];
D[x][y] = D[y][x] = getDistance(x, y);
return same[y][x] = same[x][y] = D[E][x] + D[E][y] != D[x][y] + C[h1]*2;
};
int c1 = 0, c2 = 0;
vector<int> S;
vector<vector<int>> L;
for(auto x : v) {
S.push_back(x);
if(check(S[0], x)) c1++;
else if(++c2 == c1) L.push_back(S), S.clear(), c1 = c2 = 0;
}
for(auto V : L) {
for(auto x : V) {
if(check(S[0], V[0])) c1 += check(V[0], x);
else if(!check(V[0], x)) c1 += check(S[0], x);
}
}
return c1 <= N/2 ? R : -R;
}
