#include "towns.h"
#include <bits/stdc++.h>
using namespace std;
const int N = 205;
int hubDistance(int n, int sub) {
int u = 0, v = 0;
vector<vector<int> > d(n, vector<int>(n));
vector<int> branch(n);
auto get = [&](int a, int b) {
if(a == b) return 0;
if(d[a][b]) return d[a][b];
return d[a][b] = d[b][a] = getDistance(a, b);
};
//Find 2 farthest nodes
for(int i = 0; i < n; i++) if(i != 0 && get(0, i) > get(0, u)) u = i;
for(int i = 0; i < n; i++) if(i != u && get(u, i) > get(u, v)) v = i;
//Get hub candidates on 0-u path
int lim = (get(0, u) + get(u, v) - get(0, v)) / 2;
vector<int> hub;
for(int i = 0; i < n; i++) {
branch[i] = (get(u, i) + get(0, u) - get(0, i)) / 2;
if(branch[i] <= lim) hub.emplace_back(branch[i]);
}
sort(hub.begin(), hub.end());
hub.resize(unique(hub.begin(), hub.end()) - hub.begin());
//Find hubs
int ans = get(u, v), rot = -1, rot2 = -1;
for(int pos : hub) {
int r = max(pos, get(u, v) - pos);
if(r <= ans) {
if(r == ans) swap(pos, rot), swap(pos, rot2);
else rot = pos, rot2 = -1;
ans = r;
}
}
//Boyer-Moore Majority Vote Algorithm
auto boyer_moore = [&](int p) {
auto same = [&](int a, int b) {
int ba = branch[a], bb = branch[b];
if(ba == p && bb == p)
return get(a, b) < get(0, a) + get(u, b) - get(0, u);
else return (ba < p && bb < p) || (ba > p && bb > p);
};
int cnt = 0, last = -1, total = 0;
vector<int> col(n);
for(int i = 0; i < n; i++) {
if(!cnt) last = i, ++cnt, col[i] = 0;
else if(same(i, last)) ++cnt, col[i] = 1;
else --cnt, col[i] = 2;
}
bool valid = false;
cnt = 0;
for(int i = 0; i < n; i++) {
if(!col[i]) {
++cnt;
if(same(i, last)) ++total, valid = true;
} else if(col[i] == 1) ++cnt, total += valid;
else {
total += same(i, last);
if(!--cnt) valid = false;
}
}
if(total > n / 2) return false;
else return true;
};
if(boyer_moore(rot) || (rot2 != -1 && boyer_moore(rot2))) return ans;
else return -ans;
}
