#include <bits/stdc++.h>
#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>
#include <iomanip>
#include <queue>
#include <random>
#include "towns.h"
using namespace std;
#define all(a) (a).begin(), (a).end()
#define ll long long
#define ld long double
#define ui uint64_t
#define cont(set, element) ((set).find(element) != (set).end())
#define pb push_back
#define chmin(x, y) (x = min(x, y))
#define chmax(x, y) (x = max(x, y))
/********* DEBUG *********/
template <typename T>
void outvec(const vector<T>& Z){
for (const T& x : Z)
cout << x << ' ';
cout << "\n";
}
void printVariable(const any& var) {
if (!var.has_value()) {
cout << "null";
return;
}
if (var.type() == typeid(int)) {
cout << any_cast<int>(var);
} else if (var.type() == typeid(double)) {
cout << any_cast<double>(var);
} else if (var.type() == typeid(float)) {
cout << any_cast<float>(var);
} else if (var.type() == typeid(char)) {
cout << any_cast<char>(var);
} else if (var.type() == typeid(bool)) {
cout << (any_cast<bool>(var) ? "true" : "false");
} else if (var.type() == typeid(string)) {
cout << any_cast<string>(var);
} else if (var.type() == typeid(const char*)) {
cout << any_cast<const char*>(var);
} else if (var.type() == typeid(long long)) {
cout << any_cast<long long>(var);
} else {
cout << "[unknown type]";
}
}
template<typename... Args>
void outval(Args... args) {
vector<any> variables = {args...};
for (size_t i = 0; i < variables.size(); ++i) {
printVariable(variables[i]);
if (i != variables.size() - 1) {
cout << " ";
}
}
cout << "\n";
}
#define sp << " " <<
#define fi first
#define se second
/********* DEBUG *********/
const ll MOD2 = 1e9 + 7;
const ll MOD = 998244353;
const ll inf = 1e18;
map<pair<ll,ll>, ll> memo;
int query(int a, int b){
if (b > a)
swap(a,b);
if (memo.count({a, b}))
return memo[{a,b}];
return memo[{a,b}] = getDistance(a,b);
}
int hubDistance(int N, int sub) {
memo.clear();
int f = 0, hi = 0;
for (int i = 1; i < N; i++){
ll x = query(0, i);
if (x > hi){
hi = x;
f = i;
}
}
int s = 0;
hi = 0;
for (int i = 0; i < N; i++){
if (i == f)
continue;
ll x = query(f, i);
if (x > hi){
hi = x;
s = i;
}
}
auto work = [&](ll a, ll b, ll c) -> ll {
ll ab = query(a,b);
ll bc = query(b,c);
ll ca = query(c,a);
ll abc = (ab+bc+ca)/2;
a = abc-bc, b = abc-ca, c = abc-ab;
return max({a,b,c});
};
ll ans = inf;
for (int i = 0; i < N; i++){
chmin(ans, work(f,s,i));
}
return ans;
}
