#include "towns.h"
#include <cstring>
#include <cstdio>
#include <algorithm>
#include <cassert>
#include <vector>
#include <map>
constexpr int maxn = 120;
int dp[maxn][maxn], c[maxn];
std::map<int, std::vector<int>> filhos;
int get(int i, int j) {
if(i > j) std::swap(i, j);
return dp[i][j] != -1 ? dp[i][j] : dp[i][j] = getDistance(i, j);
}
int max(int a, int b) { return a > b ? a : b; }
int min(int a, int b) { return a < b ? a : b; }
int hubDistance(int N, int sub) {
memset(dp, -1, sizeof dp);
memset(c, -1, sizeof c);
filhos.clear();
int a = 0, b = 0, dist = 0;
for(int i = 0; i < 2; i++) {
for(int j = 0; j < N; j++) {
if(a != j) {
int v = get(a, j);
if(v > dist) b = j, dist = v;
}
}
if(!i) a = b, dist = 0, b = 0;
}
int R = 0x3f3f3f3f;
for(int i = 0; i < N; i++) {
if(i == a || i == b) continue;
int d1 = get(a, i), d2 = get(b, i);
c[i] = (d1 + d2 - dist) >> 1;
R = min(R, max(d1, d2) - c[i]);
filhos[d1].push_back(i);
}
if(sub <= 2) return R;
if(sub != 4) assert(0);
int sz = 1;
bool ok = 0;
for(auto it : filhos) {
if(it.first != R && it.first != dist - R) {
sz += (int)(it.second).size();
continue;
}
if(sz > (N >> 1) || N - sz - (int)(it.second).size() > (N >> 1)) continue;
// n sei por enquanto mas sei q se chegou até aq a sub4 tá safe
ok = 1;
}
return R * (ok?1:-1);
}
