#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 (jp == R || diam-jp == R){
			if (max(xl, max(xm, xr)) <= N/2) bal = true;
		}
		xl += v.size();
	}
	if (bal) return R;
	else return -R;
}
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