#include "towns.h"
#include <bits/stdc++.h>
using namespace std;
struct dsu{
    vector<int>root;
    vector<int>siz;
    int mxsiz=1;
    dsu(int n){
        root=vector<int>(n);
        iota(root.begin(),root.end(),0);
        siz=vector<int>(n,1);
    }
    int findRoot(int x){
        if(x==root[x])
            return x;
        return root[x]=findRoot(root[x]);
    }
    bool unite(int x, int y){
        x=findRoot(x);
        y=findRoot(y);
        if(x==y)
            return 0;
        if(siz[x]<siz[y])
            swap(x,y);
        siz[x]+=siz[y];
        root[y]=x;
        mxsiz=max(mxsiz,siz[x]);
        return 1;
    }
};
int dist[115][115];
int getDist(int i, int j){
    if(dist[i][j]==-1){
        dist[i][j]=getDistance(i,j);
        dist[j][i]=dist[i][j];
    }
    return dist[i][j];
}
int hubDistance(int n, int sub) {
    for(int i = 0;i<115;i++){
        for(int j = 0;j<115;j++){
            dist[i][j]=-1;
        }
        dist[i][i]=0;
    }
    int dists[n];
    dists[0]=0;
    for(int i = 1;i<n;i++){
        dists[i] = getDist(0,i);
    }
    int u = max_element(dists,dists+n)-dists;
    dists[u]=0;
    for(int i = 0;i<n;i++){
        if(i==u)
            continue;
        dists[i]=getDist(u,i);
    }
    int v = max_element(dists,dists+n)-dists;
    int ans = dists[v];
    int rds[n];
    map<int,vector<int>>mp;
    for(int i = 0;i<n;i++){
        int d = getDist(i,v);
        int cd = (dists[i]+dists[v]-d)/2;
        int rd = (dists[i]+d-dists[v])/2;
        rds[i]=rd;
        mp[cd].push_back(i);
        cd=max(cd,dists[v]-cd);
        ans=min(ans,cd);
    }
    if(sub<=2)
        return ans;
    bool wor = 0;
    int beh = 0;
    for(pair<int,vector<int>>p:mp){
        if(p.first==ans||p.first==dists[v]-ans){
            if(beh<=n/2&&(n-beh-p.second.size())<=n/2){
                dsu ds(n);
                for(int i : p.second){
                    for(int j : p.second){
                        if(j<=i)
                            continue;
                        if(getDist(i,j)<rds[i]+rds[j]){
                            ds.unite(i,j);
                        }
                    }
                }
                if(ds.mxsiz<=n/2){
                    wor=1;
                    break;
                }
            }
        }
        beh+=p.second.size();
    }
    if(!wor)
        ans=-ans;
    return ans;
}
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