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#include <iostream>
#include <vector>
#include <cstdlib>
#include <algorithm>

template <typename T>
class BoundMatrix
{
  std::vector<T> inner_;
  unsigned int dimx_, dimy_;

public:
  BoundMatrix(unsigned int dimx, unsigned int dimy, T const& initialValue)
    : dimx_(dimx), dimy_(dimy)
  {
    inner_.resize(dimx_ * dimy_, initialValue);
  }

  T& operator()(unsigned int x, unsigned int y)
  {
    //if (x >= dimx_ || y >= dimy_)
    //  throw std::out_of_range("matrix indices out of range"); // ouch
    return inner_[dimx_ * y + x];
  }
};

int main()
{
  std::ios_base::sync_with_stdio(false);
  std::cin.tie(NULL);

  int ileTestow;
  std::cin >> ileTestow;
  for (int t = 0; t < ileTestow; ++t)
  {
    int n;
    std::cin >> n;

    std::vector<int> random_permutation;
    for (int i = 0; i < n; ++i) 
      random_permutation.push_back(i);

    std::random_shuffle(random_permutation.begin(), random_permutation.end());

    BoundMatrix<short> polaczenia = BoundMatrix<short>(n, n, n);
    for (int y = 0; y < n; ++y)
    {
      for (int x = 0; x < n; ++x)
      {
        char pol;
        std::cin >> pol;
        if (pol == '1')
          polaczenia(random_permutation[x], random_permutation[y]) = 1;
      }
    }
    for (int i = 0; i < n; ++i)
    {
      polaczenia(i, i) = 0;
    }
    BoundMatrix<short> odleglosci = polaczenia;
    BoundMatrix<short> newOdleglosci = odleglosci;
    for (int k = 0; k < n; ++k)
    {
      odleglosci = newOdleglosci;
      for (int i = 0; i < n; ++i)
      {
        for (int j = 0; j < n; ++j)
          if (odleglosci(i, k) >= 0 && odleglosci(k,j) >= 0)
            newOdleglosci(i, j) = std::min(newOdleglosci(i, j), (short)(odleglosci(i,k) + odleglosci(k,j)));
      }
    }

    short minOdlegolsc = n;
    for (int telop1 = 0; telop1 < n; ++telop1)
    {
      for (int telop2 = telop1 + 1; telop2 < n; ++telop2)
      {
        short maxOdleglosc = 0;
        for (int a1 = 0; a1 < n; ++a1)
        {
          for (int a2 = a1 + 1; a2 < n; ++a2)
          {
            short odleglosc = std::min(newOdleglosci(a1, a2), (short)(newOdleglosci(a1, telop1) + newOdleglosci(a2, telop2)));
            odleglosc = std::min(odleglosc, (short)(newOdleglosci( a1, telop2) + newOdleglosci(a2, telop1)));
            maxOdleglosc = std::max(maxOdleglosc, odleglosc);
            if (maxOdleglosc >= minOdlegolsc)
              break;
          }
          if (maxOdleglosc >= minOdlegolsc)
            break;
        }
        minOdlegolsc = std::min(minOdlegolsc, maxOdleglosc);
      }
    }
    std::cout << minOdlegolsc << "\n";
  }

  return 0;
}