#include "towns.h"
#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define pb push_back
#define mp make_pair
typedef pair<int, int> ii;
const int len = 115;
int n, s, a, b, dep[len];
map<ii, int> mym;
map<int, vector<int> > adj;
int ask(int a, int b){
if (a > b)
swap(a, b);
if (mym.count(mp(a, b)))
return mym[mp(a, b)];
return mym[mp(a, b)] = getDistance(a, b);
}
void fix_graph(){
s = 0, a = 0, b = 0;
for (int i = 0; i < n; i++)
if (ask(s, i) > ask(s, a))
a = i;
for (int i = 0; i < n; i++)
if (ask(a, i) > ask(a, b))
b = i;
adj.clear();
for (int i = 0; i < n; i++){
int pos = (ask(a, i)+ask(a, s)-ask(s, i))/2;
adj[pos].pb(i);
dep[i] = (ask(a, i)+ask(s, i)-ask(a, s))/2;
//printf("i = %d, dep = %d, pos = %d\n", i, dep[i], pos);
}
//printf("graph fixed\n");
//printf("s = %d, a = %d, b = %d\n", s, a, b);
}
void find_hubs(int &R, vector<int> &hubs){
int diam = ask(a, b);
R = diam;
hubs.clear();
for (auto &it: adj){
int pos = it.fi;
//printf("pos = %d\n", pos);
//printf("mx = %d\n", max(pos, diam-pos));
if (max(pos, diam-pos) < R)
hubs.clear(), hubs.pb(pos), R = max(pos, diam-pos);
else if (max(pos, diam-pos) == R)
hubs.pb(pos);
}
}
int hubDistance(int N, int sub) {
mym.clear(), n = N;
vector<int> hubs;
int R, balanced = 0;
fix_graph();
find_hubs(R, hubs);
auto it = adj.begin();
int lef = 0;
for (auto pos: hubs){
//printf("pos = %d\n", pos);
while ((*it).fi < pos)
lef += (*it).se.size(), it++;
int sz = (*it).se.size();
if (lef <= n/2 && sz <= n/2 && (n-lef-sz) <= n/2)
balanced = 1;
//printf("sz = %d\n", sz);
}
if (balanced)
return R;
else
return -R;
}