#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;
const int _N=555;
int d[_N][_N];
int p1(int n) {
int mx=0;
int f,s;
forn(i,n) {
if (!i) continue;
int x=getDistance(0,i);
if (x>mx) {
mx=x;
f=i;
}
}
vector<int> a(n), b(n);
mx=0;
forn(i,n) {
if (i==f) continue;
int x=getDistance(f,i);
a[i]=x;
if (x>mx) {
mx=x;
s=i;
}
}
forn(i,n) {
if (i==s) continue;
int x=getDistance(s,i);
b[i]=x;
}
int ans=inf;
map<int,int> cnt;
set<int> s1,s2;
forn(i,n) {
if (i==f || i==s) continue;
int x=a[i], y=b[i], z=a[s];
int A=(x-y+z)/2;
int B=z-A;
int C=x-A;
ans=min(ans,max(A,B));
cnt[A]++;
s1.insert(A), s2.insert(B);
}
vector<int> x,y;
for(auto&t:s1) x.pb(t);
for(auto&t:s2) y.pb(t);
reverse(all(y));
int left=1;
forn(i,s1.size()) {
if (max(x[i],y[i])==ans) {
int a=left, b=cnt[x[i]];
int c=n-a-b;
if (max({a,b,c})<=n/2) return ans;
}
left+=cnt[x[i]];
}
return -ans;
}
struct DSU {
vector<int> p,sz;
DSU(int n) {forn(i,n)p.pb(i),sz.pb(1);}
int get(int u) {return p[u]==u?u:get(p[u]);}
void uni(int u, int v){
u=get(u),v=get(v); if (u==v)return; if (sz[u]<sz[v]) swap(u,v);
p[v]=u;sz[u]+=sz[v];
}
};
int p3(int n) {
forn(i,n) {
forn(j,i) {
int x=getDistance(i,j);
d[i][j]=d[j][i]=x;
}
}
int f=0,s=0;
forn(i,n) if (d[0][i]>d[0][f]) f=i;
forn(i,n) if (d[f][i]>d[f][s]) s=i;
int ans=inf;
map<int,int> cnt;
map<int,vector<int>> q;
vector<int> ok(n);
set<int> s1,s2;
forn(i,n) {
if (i==f || i==s) continue;
int x=d[f][i], y=d[s][i], z=d[f][s];
int A=(x-y+z)/2;
int B=z-A;
int C=x-A;
ans=min(ans,max(A,B));
ok[i]=C;
cnt[A]++;
q[A].pb(i);
s1.insert(A), s2.insert(B);
}
int left=1;
vector<int> x,y;
for(auto&t:s1)x.pb(t);
for(auto&t:s2)y.pb(t);
reverse(all(y));
forn(i,s1.size()) {
if (max(x[i],y[i])==ans) {
int right=n-left-cnt[x[i]];
int mx=max(left,right);
DSU dsu(n);
for(auto&u:q[x[i]]) {
for(auto&v:q[x[i]]) {
int dist = d[u][v];
if (dist < ok[u]+ok[v]) dsu.uni(u,v);
}
}
forn(j,n) mx=max(mx,dsu.sz[j]);
if (mx<=n/2) return ans;
}
left+=cnt[x[i]];
}
return -ans;
}
int was[_N][_N];
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int p5(int n) {
int f=0,s=0;
int lim=5*n;
forn(i,n) {
if (i==0) continue; --lim;
d[0][i]=d[i][0]=getDistance(i,0);
if (d[0][i] > d[0][f]) f=i;
}
forn(i,n) {
if (i==0 || i==f) continue; --lim;
d[f][i]=d[i][f]=getDistance(i,f);
if (d[f][i] > d[f][s]) s=i;
}
map<int,vector<int>> pos;
map<int,int> cnt;
set<int> X,Y;
vector<int> di(n);
int ans=inf;
forn(i,n) {
if (i==0 || i==f || i==s) continue; --lim;
d[s][i]=d[i][s]=getDistance(i,s);
int a=d[f][i], b=d[s][i], c=d[f][s];
int x = (a-b+c)/2;
int y = c-x;
int z = a-x;
X.insert(x), Y.insert(y);
di[i]=z;
cnt[x]++;
pos[x].pb(i);
ans=min(ans,max(x,y));
}
int l=1;
vector<int> x,y;
for(auto&v:X) x.pb(v);
for(auto&v:Y) y.pb(v);
reverse(all(y));
forn(i,x.size()) {
int r=n-l-cnt[x[i]];
if (max(x[i],y[i])==ans) {
if (max({l,r,cnt[x[i]]})<=n/2) return ans;
vector<pi> asked;
int T=pos[x[i]].size();
DSU dsu(n);
forn(it,lim) {
int z=0; forn(I,T) forn(J,I) {
int a=I,b=J;
int u=pos[x[i]][a], v=pos[x[i]][b];
if (dsu.get(u)==dsu.get(v)) {
continue;
}
if (was[u][v]) {
continue;
}
z=1;
}
if (!z) break;
int a=rng()%T, b=rng()%T;
int u=pos[x[i]][a], v=pos[x[i]][b];
if (dsu.get(u)==dsu.get(v)) {
--it;
continue;
}
if (was[u][v]) {
--it;
continue;
}
int X=getDistance(u,v), Y=di[u], Z=di[v];
if (X < Y+Z) {
dsu.uni(u,v);
asked.pb({u,v});
for(auto&it:asked) {
int A=dsu.get(it.f), B=dsu.get(it.s);
was[A][B]=was[B][A]=1;
}
} else {
was[u][v]=was[v][u]=1;
}
}
int mx=max({l,r});
for(auto&v:dsu.sz) mx=max(mx,v);
if (mx<=n/2) return ans;
}
l+=cnt[x[i]];
}
return -ans;
}
int hubDistance(int n, int sub) {
if (sub<=2 || sub==4) return p1(n);
if (sub==3) return p3(n);
if (sub==5) return p5(n);
return 0;
}
