#include "towns.h"
#include<bits/stdc++.h>
using namespace std;
int hubDistance(int N, int sub) {
vector<int> d1(N, 0), d2(N, 0);
int bsf = 0, f1, f2;
for (int i=1; i<N; i++){
int d = getDistance(0, i);
if (d > bsf){
bsf = d;
f1 = i;
}
}
bsf = 0;
for (int i=0; i<N; i++){
if (i == f1) continue;
int d = getDistance(f1, i);
d1[i] = d;
if (d > bsf){
bsf = d;
f2 = i;
}
}
int R = pow(10, 9);
map<int,int> m;
for (int i=0; i<N; i++){
if (i == f1 || i == f2) continue;
int d = getDistance(f2, i);
d2[i] = d;
int l = (d1[i]+d2[i]-bsf)/2;
R = min(R, max(d1[i], d2[i])-l);
m[d1[i]-l]++;
}
bool bal = false;
for (auto it=m.begin(); it != m.end(); it++){
if (it->first == R || it->first == bsf-R){
int x1 = 1, x2 = it->second, x3 = 1;
for (auto jt=m.begin(); jt != it; jt++) x1 += jt->second;
for (auto jt=next(it); jt != m.end(); jt++) x3 += jt->second;
//cout << x1 << " " << x2 << " " << x3 << endl;
if (x1 <= N/2 && x2 <= N/2 && x3 <= N/2) bal = true;
}
}
if (bal) return R;
else return -R;
}
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