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//n^4 bru

#include <bits/stdc++.h>
using namespace std;

#define FOR(i,p,q) for(int i=(p); i<=(q); ++i)
#define ROF(i,p,q) for(int i=(p); i>=(q); --i)
#define REP(i,q) for(int i=0; i<(q); ++i)
#define pb push_back
#define as assign
#define rz resize
#define Co const
#define fi first 
#define se second 
#define all(X) X.begin(), X.end()
#define rall(X) X.rbegin(), X.rend()
#define sz(X) (int)(X.size())
#define ckmax(a,b) a=max(a,b)
#define ckmin(a,b) a=min(a,b)
#define V vector
typedef long long ll;
typedef long double ld;
typedef pair<int,int> pi;
typedef pair<ll,ll> pl;
typedef mt19937_64 mt;
#ifndef UNCLE
 typedef basic_string<bool> vb;
 typedef basic_string<int> vi;
 typedef basic_string<ll> vl;
#else
 typedef V<bool> vb;
 typedef V<int> vi;
 typedef V<ll> vl;
#endif

constexpr int INF=1e9;
int N;
V<vi> dis;
struct RG{int p,q;};
void Input(){
    cin>>N;
    dis.as(N,vi(N,INF));
    REP(v,N){
        string s; cin>>s;
        REP(u,N){
            if(u==v) dis[v][u]=0;
            else if(s[u]=='1') dis[v][u]=1;
        }
    }
}
bool IsPos(int k, mt &rng){
    vi vs;
    V<RG> rgs;
    FOR(q,0,N-1){
        vs.pb(q);
        FOR(p,0,q-1) rgs.pb({p,q});
    }
    shuffle(all(vs),rng), shuffle(all(rgs),rng);
    for(int v:vs){
        vi mxDis(N,-INF);
        bool isG=1;
        FOR(u,v+1,N-1) if(dis[v][u]>k){
            isG=0;
            REP(w,N) ckmax(mxDis[w],dis[w][u]);
        }
        if(isG) continue;
        ROF(i,sz(rgs)-1,0){
            if(dis[v][rgs[i].p]<dis[v][rgs[i].q]){
                if(dis[v][rgs[i].p]+mxDis[rgs[i].q]>k) swap(rgs[i],rgs.back()), rgs.pop_back();
            }else{
                if(dis[v][rgs[i].q]+mxDis[rgs[i].p]>k) swap(rgs[i],rgs.back()), rgs.pop_back();
            }
        }
        if(rgs.empty()) return 0;
    }
    return 1;
}
void Solve(){
    Input();
    mt rng0(14);
    mt rng(rng0());
    REP(k,N) REP(u,N) REP(v,N) ckmin(dis[u][v],dis[u][k]+dis[k][v]);
    int p=0,m,q=N;
    while(p<=q){
        m=(p+q)/2;
        if(IsPos(m,rng)) q=m-1;
        else p=m+1;
    }
    cout<<(m=q+1)<<"\n";
}
int main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0), cout.tie(0);

    int T; cin>>T;
    while(T--) Solve();
}