#include "towns.h"
#include <bits/stdc++.h>
using namespace std;
#define pb push_back
#define mp make_pair
#define pii pair<int, int>
#define fi first
#define se second
map<int, map<int, int> > mmm;
int query(int a, int b){
if (a==b)return 0;
if (!mmm[min(a, b)][max(a, b)])mmm[min(a, b)][max(a, b)]=getDistance(min(a, b), max(a, b))+1;
return mmm[min(a, b)][max(a, b)]-1;
}
int hubDistance(int n, int sub){
mmm.clear();
int mx=-1, a=0, b=0, ans=INT_MAX/2, dia=0;
for (int i=1; i<n; ++i)if (query(a, i)>mx)mx=query(a, i), b=i;
for (int i=0; i<n; ++i)dia=max(dia, query(b, i));
vector<pii> vect;
for (int i=0; i<n; ++i)vect.pb(mp((query(a, b)+query(b, i)-query(a, i))/2, i)), ans=min(ans, max(vect.back().fi, dia-vect.back().fi));
sort(vect.begin(), vect.end());
for (int i=0; i<n; ++i)if (max(vect[i].fi, dia-vect[i].fi)==ans){
int l=i, r=i, d=vect[i].fi, c=0, count=0, sz=0;
while (r+1<n&&vect[r+1].fi==d)++r;
if (l>n/2||n-r-1>n/2)continue;
for (int j=l; j<=r; ++j){
if (!count)count=1, c=vect[j].se;
else if (query(vect[j].se, c)!=query(b, vect[j].se)+query(b, c)-2*d)++count;
else --count;
}
for (int j=l; j<=r; ++j)if (query(vect[j].se, c)!=query(b, vect[j].se)+query(b, c)-2*d)++sz;
if (sz<=n/2)return ans;
i=r;
}
return -ans;
}
