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#include <iostream>
#include <iomanip>
#include <string>
#include <memory>
#include <algorithm>
#include <cassert>

// Config selector:
// 1 == Debug
// 0 == Release
#if 0

// Debug config
#define ASSERT(expr) assert(expr)
#define DBG(expr) expr

#else

// Release config
#define ASSERT(expr) do {} while (0)
#define DBG(expr) do {} while (0)

#endif

static constexpr int INF = 1'000'000'000;

/*
 * Implements n*n matrix of integers.
 */
class Matrix
{
public:
	explicit Matrix(int n, int val = 0):
		m(new int[n * n]),
		n(n)
	{
		fill(val);
	}

	void fill(int val)
	{
		std::fill(m.get(), m.get() + n * n, val);
	}

	int get_n() const
	{
		return n;
	}

	int & operator()(int row, int col)
	{
		ASSERT(row >= 0 && row < n);
		ASSERT(col >= 0 && col < n);
		return m[row * n + col];
	}

	int operator()(int row, int col) const
	{
		ASSERT(row >= 0 && row < n);
		ASSERT(col >= 0 && col < n);
		return m[row * n + col];
	}

private:
	std::unique_ptr<int[]> m; // array of size n * n
	int n;
};

std::ostream & operator<<(std::ostream & out, Matrix const & m)
{
	int const n = m.get_n();
	for (int row = 0; row < n; ++row)
	{
		for (int col = 0; col < n; ++col)
		{
			std::cout << std::setw(3) << m(row, col) << ' ';
		}
		std::cout << '\n';
	}
	return out;
}

int compute_radius(Matrix const & dist)
{
	int const n = dist.get_n();
	int r = INF;
	for (int row = 0; row < n; ++row)
	{
		int row_max_dist = 0;
		for (int col = 0; col < n; ++col)
		{
			row_max_dist = std::max(row_max_dist, dist(row, col));
		}
		r = std::min(r, row_max_dist);
	}
	return r;
}

int compute_max_distance(Matrix const & dist)
{
	int const n = dist.get_n();
	int total_max_dist = 0;
	for (int row = 0; row < n; ++row)
	{
		int row_max_dist = 0;
		for (int col = 0; col < n; ++col)
		{
			row_max_dist = std::max(row_max_dist, dist(row, col));
		}
		total_max_dist = std::max(total_max_dist, row_max_dist);
	}
	return total_max_dist;
}

// Computes matrix of distances between all pairs of vertices.
Matrix floyd_warshall(Matrix const & edges)
{
	int const n = edges.get_n();
	Matrix dist(n, INF);
	for (int row = 0; row < n; ++row)
	{
		for (int col = 0; col < n; ++col)
		{
			int const weight = edges(row, col);
			if (weight)
				dist(row, col) = weight;
		}
	}
	for (int row = 0; row < n; ++row)
	{
		dist(row, row) = 0;
	}
	for (int k = 0; k < n; ++k)
	{
		for (int row = 0; row < n; ++row)
		{
			for (int col = 0; col < n; ++col)
			{
				dist(row, col) = std::min(dist(row, col),
						// make sure it won't exceed INF
						std::min(INF, dist(row, k) + dist(k, col)));
			}
		}
	}
	return dist;
}

// Returns a new graph, with vertices to_merge1 and to_merge2 merged into one.
Matrix compute_teleport_edges(Matrix const & old_edges, int to_merge1, int to_merge2)
{
	if (to_merge1 > to_merge2)
		std::swap(to_merge1, to_merge2);
	ASSERT(to_merge1 < to_merge2);
	int const n = old_edges.get_n();

	// The new graph has the following vertices:
	// v_new in [0; to_merge2-1]: take vertex of idx==v_new from the old graph,
	//                     but if v_new==to_merge1 then consider also edges of to_merge2 from the old graph
	// v_new in [to_merge2; n-2]: take vertex of idx==v_new+1 from the old graph
	Matrix new_edges(n - 1);
	for (int v1_new = 0; v1_new < n - 1; ++v1_new)
	{
		for (int v2_new = 0; v2_new < n - 1; ++v2_new)
		{
			// Consider edge (v1_new, v2_new) in the new graph.
			int new_edge_weight = 0;
			if (v1_new != v2_new)
			{
				int const v2_old = v2_new < to_merge2 ? v2_new : v2_new + 1;
				int const v1_old = v1_new < to_merge2 ? v1_new : v1_new + 1;
				if (v1_new == to_merge1)
				{
					new_edge_weight = old_edges(to_merge1, v2_old) || old_edges(to_merge2, v2_old);
				}
				else if (v2_new == to_merge1)
				{
					new_edge_weight = old_edges(v1_old, to_merge1) || old_edges(v1_old, to_merge2);
				}
				else
				{
					new_edge_weight = old_edges(v1_old, v2_old);
				}
			}
			new_edges(v1_new, v2_new) = new_edge_weight;
		}
	}

	return new_edges;
}

void read_and_solve()
{
	int n;
	std::cin >> n >> std::ws;
	DBG(std::cout << "=== read_and_solve, n=" << n << " ===\n");

	Matrix edges(n);

	// Read graph.
	std::string str;
	for (int row = 0; row < n; ++row)
	{
		std::getline(std::cin, str);
		ASSERT((int)str.size() == n);
		for (int col = 0; col < n; ++col)
		{
			char chr = str[col];
			ASSERT(chr == '0' || chr == '1');
			if (chr == '1')
			{
				ASSERT(row != col);
				edges(row, col) = 1;
			}
		}
	}
	DBG(std::cout << "edges:\n" << edges);

	Matrix const dist = floyd_warshall(edges);
	DBG(std::cout << "dist:\n" << dist);

	int const r = compute_radius(dist);
	DBG(std::cout << "radius: " << r << '\n');

	int min_tank_size = INF;
	int num_v0_considered = 0;
	for (int row = 0; row < n; ++row)
	{
		int row_max_dist = 0;
		for (int col = 0; col < n; ++col)
		{
			row_max_dist = std::max(row_max_dist, dist(row, col));
		}
		if (row_max_dist == r)
		{
			int const v0 = row;
			// Now find v1.
			int num_v1_considered = 0;
			for (int col = 0; col < n; ++col)
			{
				if (dist(v0, col) == r/2)
				{
					int const v1 = col;
					// Now find v2, but this time consider just one candidate.
					for (int v2 = 0; v2 < n; ++v2)
					{
						if (dist(v1, v2) == r)
						{
							// Create graph with v1 and v2 merged.
							Matrix const edges_with_teleport = compute_teleport_edges(edges, v1, v2);
							DBG(std::cout << "\n== candidate graph with vertices " << v1 << " and " << v2
								<< " merged ==\n" << edges_with_teleport);

							Matrix const dist_with_teleport = floyd_warshall(edges_with_teleport);
							DBG(std::cout << "candidate graph radius: " << compute_radius(dist_with_teleport) << '\n');

							int const candidate_tank_size = compute_max_distance(dist_with_teleport);
							DBG(std::cout << "candidate tank size: " << candidate_tank_size << '\n');
							min_tank_size = std::min(min_tank_size, candidate_tank_size);

							// We consider just one candidate for v2.
							break;
						}
					}

					// End of v1 processing.
					if (++num_v1_considered == 2)
					{
						// We consider only 2 candidates for v1.
						break;
					}
				}
			}

			// End of v0 processing.
			if (++num_v0_considered == 2)
			{
				// We consider only 2 candidates for v0.
				break;
			}
		}
	}

	DBG(std::cout << "\nRESULT: minimal tank size is: ");
	std::cout << min_tank_size << '\n';
	DBG(std::cout << '\n');
}

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

	int t;
	std::cin >> t >> std::ws;
	for (int i = 0; i < t; ++i)
	{
		read_and_solve();
	}
}