#include "towns.h"
#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define pf printf
#define pb push_back
#define sz(x) ((int)x.size())
#define all(x) x.begin(),x.end()
typedef vector<int> vi;
typedef pair<int,int> ii;
int cnt;
map<int,int> memo[150];
inline int ask(int a,int b){
if(a==b)return 0;
if(memo[a].find(b)!=memo[a].end())return memo[a][b];
++cnt;
return memo[a][b]=memo[b][a]=getDistance(a,b);
}
int hubDistance(int N,int sub){
cnt=0;
for(int i=0;i<N;++i)memo[i].clear();
int a=0,b=0,diam=0;
for(int i=0;i<N;++i)if(ask(a,i)>ask(a,b))b=i;
for(int i=0;i<N;++i)diam=max(diam,ask(b,i));
int ans=diam;
vector<ii> v;
for(int i=0;i<N;++i){
int ab=ask(a,b),ai=ask(a,i),bi=ask(i,b);
int db=(ab+bi-ai)/2;
v.pb({db,i});
ans=min(ans,max(db,diam-db));
}
/*
sort(all(v));
for(int i=0;i<N;++i){
if(max(v[i].fi,ask(a,b)-v[i].fi)!=ans)continue;
int l=i,r=i;
while(r<N-1&&v[r].fi==v[r+1].fi)++r;
if(l>N/2||N-r>N/2)continue;
vector<vi> cur,nxt,dead;
for(int i=l;i<=r;++i)cur.pb({v[i].se});
int rep=-1;
while(!cur.empty()){
for(int i=0;i<sz(cur);i+=2){
if(i+1==sz(cur)){
rep=cur[i].se;
}
else{
int x=cur[i].se,y=cur[i+1].se;
if(ask(a,x)+ask(a,y)-ask(x,y)>2*v[l].fi){
nxt.pb(cur[i]);
}
}
}
swap(cur,nxt);
nxt.clear();
}
if(rep==-1)return ans;
int num=0;
for(int i=l;i<=r;++i){
int x=rep,y=i;
if(ask(a,x)+ask(a,y)-ask(x,y)>2*v[l].fi)++num;
}
if(num<=N/2)return ans;
}
*/
return -ans;
}
