#include "towns.h"
#include<bits/stdc++.h>
using namespace std;
const int MAXN = 110;
int dist[MAXN][MAXN];
int hubDistance(int N, int sub) {
int p1 = 0, p2 = 0;
int maxi = 0;
map<pair<int, int>, int> marc;
for(int i = 0; i < N; i++){
if(marc[make_pair(0, i)] == 0){
marc[make_pair(0, i)] = 1;
marc[make_pair(i, 0)] = 1;
dist[i][0] = dist[0][i] = getDistance(0, i);
}
if(dist[i][0] > maxi) p1 = i, maxi = dist[i][0];
}
maxi = 0;
for(int i = 0; i < N; i++){
if(marc[make_pair(p1, i)] == 0){
marc[make_pair(p1, i)] = 1;
marc[make_pair(i, p1)] = 1;
dist[i][p1] = dist[p1][i] = getDistance(p1, i);
}
if(dist[p1][i] > maxi) maxi = dist[p1][i], p2 = i;
}
for(int i = 0; i < N; i++){
if(marc[make_pair(p2, i)] == 0){
marc[make_pair(p2, i)] = 1;
marc[make_pair(i, p2)] = 1;
dist[i][p2] = dist[p2][i] = getDistance(p2, i);
}
}
int diam = dist[p1][p2];
int ans = MAXN;
for(int i = 0; i < N; i++){
int x = (diam + dist[p1][i] - dist[p2][i]) / 2;
ans = min(ans, max(x, diam - x));
}
if(sub <= 2) return ans;
int lSize = 0, rSize = 0;
vector<int> lMid, rMid;
for(int i = 0; i < N; i++){
int x = (diam + dist[p1][i] - dist[p2][i]) / 2;
if(x < min(ans, diam - ans)) lSize++;
else if(x == min(ans, diam - ans)) lMid.push_back(i);
else if(x == max(ans, diam - ans)) rMid.push_back(i);
else rSize++;
}
if(sub <= 4){
if(lSize > N / 2 || rSize > N / 2 || lMid.size() > N / 2 || rMid.size() > N / 2) return -ans;
return ans;
}
if(lSize > N / 2 || rSize > N / 2) return -ans;
else if(lMid.size() > N / 2){
stack<int> pilha;
for(int i = 0; i < lMid.size(); i++){
if(pilha.empty()) pilha.push(lMid[i]);
else{
int aux = dist[p1][pilha.top()];
if(marc[make_pair(pilha.top(), lMid[i])] == 0){
marc[make_pair(pilha.top(), lMid[i])] = 1;
marc[make_pair(lMid[i], pilha.top())] = 1;
dist[lMid[i]][pilha.top()] = dist[pilha.top()][lMid[i]] = getDistance(pilha.top(), lMid[i]);
}
int x = (aux + dist[p1][lMid[i]] - dist[lMid[i]][pilha.top()]) / 2;
if(x == min(ans, diam - ans)) pilha.pop();
else pilha.push(lMid[i]);
}
}
if(pilha.empty()) return ans;
int k = pilha.top();
int cnt = 0;
for(int i = 0; i < lMid.size(); i++){
int aux = dist[p1][k];
if(marc[make_pair(k, lMid[i])] == 0){
marc[make_pair(k, lMid[i])] = 1;
marc[make_pair(lMid[i], k)] = 1;
dist[lMid[i]][k] = dist[k][lMid[i]] = getDistance(k, lMid[i]);
}
int x = (aux + dist[p1][lMid[i]] - dist[k][lMid[i]]) / 2;
if(x > min(ans, diam - ans)) cnt++;
}
if(cnt > N / 2) return -ans;
return ans;
}
else if(rMid.size() > N / 2){
stack<int> pilha;
for(int i = 0; i < rMid.size(); i++){
if(pilha.empty()) pilha.push(rMid[i]);
else{
int aux = dist[p1][pilha.top()];
if(marc[make_pair(pilha.top(), rMid[i])] == 0){
marc[make_pair(pilha.top(), rMid[i])] = 1;
marc[make_pair(rMid[i], pilha.top())] = 1;
dist[lMid[i]][pilha.top()] = dist[pilha.top()][rMid[i]] = getDistance(pilha.top(), rMid[i]);
}
int x = (aux + dist[p1][rMid[i]] - dist[rMid[i]][pilha.top()]) / 2;
if(x == max(ans, diam - ans)) pilha.pop();
else pilha.push(rMid[i]);
}
}
if(pilha.empty()) return ans;
int k = pilha.top();
int cnt = 0;
for(int i = 0; i < rMid.size(); i++){
int aux = dist[p1][k];
if(marc[make_pair(k, rMid[i])] == 0){
marc[make_pair(k, rMid[i])] = 1;
marc[make_pair(rMid[i], k)] = 1;
dist[rMid[i]][k] = dist[k][rMid[i]] = getDistance(k, rMid[i]);
}
int x = (aux + dist[p1][rMid[i]] - dist[k][rMid[i]]) / 2;
if(x > max(ans, diam - ans)) cnt++;
}
if(cnt > N / 2) return -ans;
return ans;
}
return ans;
}
