#include "towns.h"
#include<bits/stdc++.h>
using namespace std;
map<pair<int,int>,int> res;
int getDist(int a, int b){
if (a == b) return 0;
if (a > b) swap(a, b);
if (res.find({a, b}) == res.end()) res[{a, b}] = getDistance(a, b);
return res[{a, b}];
}
int hubDistance(int N, int sub){
res.clear();
int bsf = 0, f1, f2;
for (int i=1; i<N; i++){
int d = getDist(0, i);
if (d > bsf){
bsf = d;
f1 = i;
}
}
bsf = 0;
for (int i=0; i<N; i++){
if (i == f1) continue;
int d = getDist(f1, i);
if (d > bsf){
bsf = d;
f2 = i;
}
}
int diam = getDist(f1, f2);
int j0 = (getDist(f1, 0)+getDist(f1, f2)-getDist(f2, 0))/2;
map<int,vector<int>> m;
int R = pow(10, 9);
for (int i=0; i<N; i++){
int jp = (getDist(f1, 0)+getDist(f1, i)-getDist(0, i))/2;
jp = min(j0, jp);
m[jp].push_back(i);
R = min(R, max(jp, diam-jp));
}
int xl = 0, xm, xr = N;
bool bal = false;
for (auto [jp, v] : m){
xr -= v.size();
xm = v.size();
if (max(xl, max(xm, xr)) <= N/2) bal = true;
xl += v.size();
}
if (bal) return R;
else return -R;
}
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