#include "towns.h"
#include <bits/stdc++.h>
#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")
using namespace std;
#define X first
#define Y second
#define pb push_back
typedef pair<int, int> ii;
typedef long long ll;
const int maxn = 120;
int m, n;
int dist0[maxn];
int distu[maxn];
int add[maxn], bran[maxn];
map<int, int> cnt;
map<int, vector<int> > faker;
map<int, int> on;
int hub;
bool isSame(int u, int v)
{
if(u == -1 || v == -1) return false;
return getDistance(u, v) != dist0[u]+dist0[v]-2*hub;
}
int hubDistance(int N, int sub)
{
memset(add, 0, sizeof add);
memset(bran, 0, sizeof bran);
cnt.clear();
faker.clear();
on.clear();
n = N;
int best = 0, dat = -1;
for(int i = 1; i< N; i++)
{
dist0[i] = getDistance(0, i);
if(dist0[i]> best)
{
best = dist0[i];
dat = i;
}
}
int U = dat;
best = 0; dat = -1;
for(int i = 0; i< N; i++)
{
if(i == U) continue;
if(i == 0)
{
distu[0] = dist0[U];
}
distu[i] = getDistance(U, i);
if(distu[i]> best)
{
best = distu[i];
dat = i;
}
}
int V = dat;
int diam = distu[V];
// printf("(%d->%d) %d\n", U, V, dist[V]);
distu[0] = dist0[U];
for(int i = 0; i< N; i++)
{
if(i == U || i == 0) continue;
int br = dist0[i]+distu[i]-dist0[U];
br /= 2;
int pos = distu[i]-br;
add[i] = pos;
bran[i] = br;
cnt[pos]++;
faker[pos].pb(i);
}
int rad = diam;
bool good = false;
int cm = 1;
for(auto kk : cnt)
{
int x = kk.X;
rad = min(rad, max(x, diam-x));
}
vector<int> hubs;
for(auto kk : cnt)
{
int x = kk.X, y = kk.Y;
if(rad == max(x, diam-x))
{
hubs.pb(x);
if(max(max(cm, cnt[x]), n-cm-cnt[x]) <= n/2) good = true;
}
cm += cnt[x];
on[x] = cm;
}
vector<int> doubt;
while(!hubs.empty())
{
int u = hubs.back(); hubs.pop_back();
if(max(on[u]-cnt[u], n-on[u])> n/2) continue;
if(max(cnt[u], max(on[u]-cnt[u], n-on[u]))<= n/2) return rad;
doubt.pb(u);
}
if(doubt.empty()) return -rad;
hub = doubt[0];
assert(cnt[hub]> n/2);
int tweet = n-cnt[hub];
int cand = -1;
for(int i = 0; i< (int) faker[hub].size(); i++)
{
if(tweet == 0)
{
cand = faker[hub][i];
}
if(isSame(cand, faker[hub][i])) tweet++;
else tweet--;
}
int res = 0;
for(int i = 0; i< (int) faker[hub].size(); i++)
{
res += isSame(cand, faker[hub][i]);
}
if(res<= n/2)
{
return rad;
}
return -rad;
}
