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// Karol Kosinski 2025
#include <bits/stdc++.h>
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define FR_(i,a,b) for(int i=(a),_b=(b);i<=_b;++i)
#define FD_(i,b,a) for(int i=(b),_a=(a);i>=_a;--i)
#define ALL(c) (c).begin(),(c).end()
#define SIZE(c) int((c).size())
#define X first
#define Y second
#define endl '\n'
#define NAM(x) #x,'=',x
using namespace std;
using LL = long long;
using ULL = unsigned long long;
using PII = pair<int, int>;
using TIII = tuple<int, int, int>;
template<class...T> void _cout(T...a){(cout<<...<<a);}

#ifndef ENABLE_DEBUG
#define DEB(k,p,f,x...)
#else
#define DEB(k,p,f,x...) {if(k)_cout("------",setw(4),__LINE__," : ",__FUNCTION__,endl);if(p)f(x);}
#endif
#define DEBF(f,x...)    DEB(1,1,f,x)
#define DEBL            DEBF(void,0)
#define DEBC(p,x...)    DEB(0,p,_cout,x)
#define DEBUG(x...)     DEBC(1,x)

constexpr int NX = 405;

namespace FloydWarshall
{
    static constexpr int INFTY = 1e9 + 1;

    int n, D[NX][NX];

    void init(int n0)
    {
        n = n0;
        FOR(u,0,n) FOR(v,0,n) D[u][v] = ( u == v ) ? 0 : INFTY;
    }

    void add(int u, int v, int w) { D[u][v] = w; }

    void run()
    {
        FOR(k,0,n) FOR(i,0,n) FOR(j,0,n) if ( D[i][j] > D[i][k] + D[k][j] )
            D[i][j] = D[i][k] + D[k][j];
    }
};

void print_fw(int n)
{
    FOR(i,0,n)
    {
        DEBUG( "** ");
        FOR(j,0,n)
        {
            DEBUG( FloydWarshall::D[i][j], " " );
        }
        DEBUG(endl);
    }
}

void solve()
{
    int n;
    cin >> n;
    FloydWarshall::init(n);
    FOR(i,0,n)
    {
        string s; cin >> s;
        FOR(j,0,n) if ( s[j] == '1' )
        {
            FloydWarshall::add(i, j, 1);
            FloydWarshall::add(j, i, 1);
        }
    }
    FloydWarshall::run();
    auto& S = FloydWarshall::D;
    DEBF( print_fw, n );
    DEBL;

    int dmax = FloydWarshall::INFTY;
    FOR(i,0,n)
    {
        FOR(j,i+1,n)
        {
            int d = 0;
            FOR(u,0,n) FOR(v,u+1,n)
            {
                d = max( d, min( S[u][v], min( S[u][i] + S[j][v], S[u][j] + S[i][v] ) ) );
            }
            dmax = min( dmax, d );
        }
    }
    cout << dmax << endl;
}

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    int z; cin >> z;
    while ( z -- ) solve();
    return 0;
}