#include "towns.h"
#include<bits/stdc++.h>
using namespace std;
int dis0[200], disX[200], disY[200];
vector<int> mid, mid2;
int X, Y;
bool checkdiff(int a, int b) {
int ad = (disX[Y] + disX[a] + disY[a]) / 2 - disX[Y];
int bd = (disX[Y] + disX[b] + disY[b]) / 2 - disX[Y];
if(getDistance(a, b) == ad+bd) return true;
return false;
}
int hubDistance(int N, int sub) {
X = 1;
for(int i=1; i<N; i++) {
dis0[i] = getDistance(0, i);
if(dis0[i] > dis0[X]) {
X = i;
}
}
Y = 0;
for(int i=0; i<N; i++) {
if(i==X) continue;
disX[i] = getDistance(X, i);
if(disX[i] > disX[Y]) {
Y = i;
}
}
// diameter: X to Y
for(int i=0; i<N; i++) {
if(i==Y) continue;
disY[i] = getDistance(Y, i);
}
int ans = 1e9;
int C = 0;
for(int i=0; i<N; i++) {
if(i==X || i==Y) continue;
int sum = (disX[Y] + disX[i] + disY[i]) / 2;
int tmp = max(sum - disX[i], sum - disY[i]);
if(tmp < ans) {
C = i;
ans = tmp;
}
}
int sumC = (disX[Y] + disX[C] + disY[C]) / 2;
mid.clear();
int compX = 1, compY = 1, oth = N - 2;
for(int i=0; i<N; i++) {
if(i==X || i==Y) continue;
int sum = (disX[Y] + disX[i] + disY[i]) / 2;
if(sum - disY[i] < sumC - disY[C]) {
compX++;
oth--;
} else if(sum - disX[i] < sumC - disX[C]) {
compY++;
oth--;
} else mid.push_back(i);
}
if(sub <= 2) return ans;
if(sub==4) {
if(compX <= N/2 && compY <= N/2 && oth <= N/2) return ans;
else return -ans;
} else if(sub >= 3) {
mid2 = mid;
while(mid.size() >= 2) {
if(checkdiff(mid[mid.size()-1], mid[mid.size()-2])) {
mid.pop_back();
mid.pop_back();
} else {
mid.pop_back();
}
}
if(mid.size() == 1) {
int cnt = 0;
for(int i:mid2) {
if(!checkdiff(i, mid[0])) {
cnt++;
}
}
if(cnt > N/2 || compX > N/2 || compY > N/2) return -ans;
else return ans;
}
if(compX > N/2 || compY > N/2) return -ans;
return ans;
}
return ans;
}
