#include "towns.h"
#include <bits/stdc++.h>
using namespace std;
#define forn(i,n) for(int i=0;i<n;++i)
#define pb push_back
#define all(x) x.begin(), x.end()
#define pi pair<int,int>
#define f first
#define s second
const int inf=1e9+9;
int p1(int n) {
vector<int> a(n), b(n), c(n);
int f=0;
forn(i,n) {
a[i]=getDistance(0,i);
if (a[i]>a[f]) f=i;
}
int s=0;
forn(i,n) {
b[i]=getDistance(f,i);
if (b[i]>b[s]) s=i;
}
forn(i,n) {
c[i]=getDistance(s,i);
}
set<int> st;
vector<int> d(n);
map<int,vector<int>> ok;
forn(i,n) {
if (i==f || i==s) continue;
int x=b[i], y=c[i], z=b[s];
int A=(x-y+z)/2;
d[i]=x-A;
st.insert(A);
ok[A].pb(i);
}
int ans=inf;
for(auto&x:st) {
int y=b[s]-x;
ans=min(ans,max(x,y));
}
int l=1;
for(auto&x:st) {
int y=b[s]-x;
if (max(x,y)!=ans) {
l+=ok[x].size();
continue;
}
int r=n-ok[x].size()-l;
if (max(l,r)>n/2) continue;
int t=ok[x].size();
if (t<=n/2) return ans;
}
return -ans;
}
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int p5(int n) {
vector<int> a(n), b(n), c(n);
int f=0;
forn(i,n) {
a[i]=getDistance(0,i);
if (a[i]>a[f]) f=i;
}
int s=0;
forn(i,n) {
b[i]=getDistance(f,i);
if (b[i]>b[s]) s=i;
}
forn(i,n) {
c[i]=getDistance(s,i);
}
set<int> st;
vector<int> d(n);
map<int,vector<int>> ok;
forn(i,n) {
if (i==f || i==s) continue;
int x=b[i], y=c[i], z=b[s];
int A=(x-y+z)/2;
d[i]=x-A;
st.insert(A);
ok[A].pb(i);
}
int ans=inf;
for(auto&x:st) {
int y=b[s]-x;
ans=min(ans,max(x,y));
}
int l=1;
int last=-1;
for(auto&x:st) {
l+=ok[last].size(); last=x;
int y=b[s]-x;
if (max(x,y)!=ans) continue;
int r=n-ok[x].size()-l;
if (max(l,r)>n/2) continue;
int t=ok[x].size();
if (t<=n/2) return ans;
vector<pi> a,b;
for(auto&v:ok[x]) a.pb({v,1});
while (a.size()>1) {
int k = a.size();
for (int i=0; i+1<a.size(); i+=2) {
int z = getDistance(a[i].f,a[i+1].f);
int x = d[a[i].f], y = d[a[i+1].f];
if (z==x+y) {
if (a[i].s > a[i+1].s) b.pb(a[i]);
else b.pb(a[i+1]);
continue;
}
b.pb({a[i].f,a[i].s+a[i+1].s});
}
if (k&1) b.pb(a.back());
a=b;
b.clear();
}
int u=a[0].f;
int sz=0;
for(auto&v:ok[x]) {
int z = getDistance(u,v);
int x = d[u], y = d[v];
if (z<x+y) ++sz;
}
if (sz<=n/2) return ans;
}
return -ans;
}
int hubDistance(int n, int sub) {
if (sub<=2 || sub==4) return p1(n);
if (sub>=3) return p5(n);
return 0;
}
