/*
ID: varunra2
LANG: C++
TASK: towns
*/
#include <bits/stdc++.h>
#include "towns.h"
using namespace std;
#ifdef DEBUG
#include "lib/debug.h"
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define debug_arr(...) \
cerr << "[" << #__VA_ARGS__ << "]:", debug_arr(__VA_ARGS__)
#pragma GCC diagnostic ignored "-Wsign-compare"
//#pragma GCC diagnostic ignored "-Wunused-parameter"
//#pragma GCC diagnostic ignored "-Wunused-variable"
#else
#define debug(...) 42
#endif
#define EPS 1e-9
#define IN(A, B, C) assert(B <= A && A <= C)
#define INF (int)1e9
#define MEM(a, b) memset(a, (b), sizeof(a))
#define MOD 1000000007
#define MP make_pair
#define PB push_back
#define all(cont) cont.begin(), cont.end()
#define rall(cont) cont.end(), cont.begin()
#define x first
#define y second
const double PI = acos(-1.0);
typedef long long ll;
typedef long double ld;
typedef pair<int, int> PII;
typedef map<int, int> MPII;
typedef multiset<int> MSETI;
typedef set<int> SETI;
typedef set<string> SETS;
typedef vector<int> VI;
typedef vector<PII> VII;
typedef vector<VI> VVI;
typedef vector<string> VS;
#define rep(i, a, b) for (int i = a; i < (b); ++i)
#define trav(a, x) for (auto& a : x)
#define sz(x) (int)(x).size()
typedef pair<int, int> pii;
typedef vector<int> vi;
#pragma GCC diagnostic ignored "-Wsign-compare"
// util functions
// we are rooting the tree at leaf 0
int n;
const int mx = 150;
int vals[mx][mx];
map<PII, int> mp;
// int getDistance(int i, int j) { return vals[i][j]; }
int gt(int i, int j) {
if (i > j) swap(i, j);
if (i == j) return 0;
if (mp[MP(i, j)]) return mp[MP(i, j)];
mp[MP(i, j)] = getDistance(i, j);
return mp[MP(i, j)];
}
int rootdist(int d1, int d2, int dtot) {
// d1 + d2 - 2 * dlca = dtot
// (d1 + d2 - dtot)/2 = dlca
return (d1 + d2 - dtot) / 2;
}
int leafdist(int d1, int d2, int dtot) {
// what is the dist(d1, dlca)
// dist(d1, dlca) = d1 - rootdist(dlca)
return d1 - rootdist(d1, d2, dtot);
}
void calc(int from, VI& d) {
for (int i = 0; i < n; i++) {
if (i == from) continue;
d[i] = gt(from, i);
}
}
int ind1;
int ind2;
VI d0;
VI d1;
VI d2; // we won't be using this
VI lcadists;
void init() {
mp.clear();
d0.clear();
d1.clear();
d2.clear();
lcadists.clear();
d0.assign(n, 0);
d1.assign(n, 0);
d2.assign(n, 0);
lcadists.assign(n, 0);
}
int find(int lcdist) {
int val1 = d0[ind1] - lcdist;
int val2 = d1[ind2] - val1;
int cur = max(val1, val2);
return cur;
}
VI findHubs() {
// we will use 2n - 3 queries to find the hubs/radius/center
calc(0, d0);
ind1 = max_element(all(d0)) - d0.begin();
calc(ind1, d1);
ind2 = max_element(all(d1)) - d1.begin();
// diameter is from ind1 -> ind2
// hub lies on the path from 0 -> ind1 && ind1 -> ind2
// so since we rooted the tree at 0
// the hub lies on the path from ind1 -> lca(ind1, ind2)
for (int i = 0; i < n; i++) {
lcadists[i] = rootdist(d0[ind1], d0[i], d1[i]);
}
int mx = lcadists[ind2];
VI ret;
int mn = 2 * INF;
MPII mp;
sort(all(lcadists));
lcadists.resize(unique(all(lcadists)) - lcadists.begin());
for (int i = 0; i < sz(lcadists); i++) {
if (lcadists[i] < mx) continue;
int cur = find(lcadists[i]);
if (cur < mn) {
ret.clear();
ret.PB(lcadists[i]);
mn = cur;
} else if (cur == mn)
ret.PB(lcadists[i]);
}
return ret;
}
int hubDistance(int n, int sub) {
::n = n;
init();
auto use = findHubs();
return find(use[0]);
}
// int main() {
// #ifndef ONLINE_JUDGE
// freopen("towns.in", "r", stdin);
// freopen("towns.out", "w", stdout);
// #endif
// cin.sync_with_stdio(0);
// cin.tie(0);
// int subbb;
// cin >> subbb;
// int t;
// cin >> t;
// while (t--) {
// int n;
// cin >> n;
// for (int i = 0; i < n; i++) {
// for (int j = 0; j < n; j++) {
// cin >> vals[i][j];
// }
// }
// cout << hubDistance(n, 2) << '\n';
// }
// return 0;
// }
