#include "towns.h"
#include <bits/stdc++.h>
using namespace std;
const int mxN = 111;
int arr[mxN];
int dist[mxN][mxN];
int numHub = 0;
int lcadist[mxN];
int n;
int s, t;
/*int indist[mxN][mxN];
int queries = 0;
int getDistance(int a, int b) {
queries++;
return indist[a][b];
}*/
int getdist(int a, int b) {
if(a==b)return 0;
if(dist[a][b]==-1) {
return dist[a][b] = dist[b][a] = getDistance(a, b);
}
return dist[a][b];
}
bool solve(int hub) {
vector<int> stk;
vector<int> bkt;
stk.push_back(0);
function<bool(int, int)> compare = [&](int a, int b) {
if(lcadist[a] < lcadist[hub] && lcadist[b] < lcadist[hub]) {
return true;
}else if(lcadist[a] > lcadist[hub] && lcadist[b] > lcadist[hub]) {
return true;
}else if(lcadist[a] == lcadist[hub] && lcadist[b] == lcadist[hub]) {
if(getdist(s, a) + getdist(s, b) - getdist(a, b) > 2 * lcadist[hub])return true;
}
return false;
};
for(int i = 1; i < n; ++i) {
if(compare(stk.back(), i)) {
bkt.push_back(i);
}else {
stk.push_back(i);
if(bkt.size()) {
stk.push_back(bkt.back());
bkt.pop_back();
}
}
}
int T = stk.back();
stk.pop_back();
while(stk.size()) {
int lst = stk.back();
stk.pop_back();
if(compare(lst, T)) {
if(stk.size()==0) {
bkt.push_back(lst);
}else {
stk.pop_back();
}
}else {
if(bkt.size()==0) {
return true;
}
bkt.pop_back();
}
}
if(bkt.size())return false;
return true;
}
int hubDistance(int N, int sub) {
n = N;
memset(dist, -1, sizeof(dist));
for(int i = 1, mxdist = 0; i < n; ++i) {
if(getdist(0, i) > mxdist) {
mxdist = getdist(0, i);
s = i;
}
}
for(int i = 0, mxdist = 0; i < n; ++i) {
if(i^s) {
if(getdist(s, i) > mxdist) {
mxdist = getdist(s, i);
t = i;
}
}
}
int hub[2];
int hubcnt = 0;
int R = 0x3f3f3f3f;
for(int i = 0; i < n; ++i) {
lcadist[i] = (getdist(s, i) + getdist(s, 0) - getdist(i, 0)) / 2;
if(max(lcadist[i], getdist(s, t) - lcadist[i]) < R) {
R = max(lcadist[i], getdist(s, t) - lcadist[i]);
hubcnt = 1;
hub[0] = i;
}else if(max(lcadist[i], getdist(s, t) - lcadist[i]) == R){
hubcnt = 2;
hub[1] = i;
}
}
//cout<<hubcnt<<"\n";
if(sub <= 2) {
return R;
}
bool balanced = false;
for(int i = 0; i < hubcnt; ++i) {
balanced |= solve(hub[i]);
}
return (balanced ? 1 : -1) * R;
}
