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

vector<int> graph[407];
int odl[407][407];
int maksss[407][407][407];//maks odl zagladajac start w i, drugi portal w j, dla odl od i >= k
pair<int, int> maksodl[407];
string graf[407];
int n;

void bfs(int skad)
{
	odl[skad][skad] = 0;
	queue<int> q;
	q.push(skad);
	while (!q.empty())
	{
		int cur = q.front();
		q.pop();
		for (auto x : graph[cur])
		{
			if (odl[skad][x] == INT_MAX)
			{
				odl[skad][x] = odl[skad][cur] + 1;
				q.push(x);
			}
		}
	}
}

bool spr(int sr)
{
	for (int p1 = 1; p1 <= n; p1++)
	{
		for (int p2 = 1; p2 <= n; p2++)
		{
			bool czyok = true;
			for (int start = 1; start <= n; start++)
			{
				if (!(sr - odl[start][p1] >= maksss[start][p2][sr + 1] || sr - odl[start][p2] >= maksss[start][p1][sr + 1]))
				{
					czyok = false;
					start = n + 7;
				}
			}
			if (czyok)
			{
				//cout << p1 << " " << p2 << endl;
				return true;
			}
		}
	}
	return false;
}

int main()
{
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	int t;
	cin >> t;
	while (t--)
	{
		cin >> n;
		int odpo = n;
		for (int i = 1; i <= n; i++)
		{
			for (int j = 1; j <= n; j++)
			{
				odl[i][j] = INT_MAX;
			}
		}
		for (int i = 1; i <= n; i++)
		{
			graph[i].clear();
			cin >> graf[i];
		}
		for (int i = 1; i <= n; i++)
		{
			for (int j = 1; j <= n; j++)
			{
				if (graf[i][j - 1] == '1')
				{
					graph[i].push_back(j);
					graph[j].push_back(i);
				}
			}
		}
		for (int i = 1; i <= n; i++)
		{
			bfs(i);
		}
		for (int i = 1; i <= n; i++)
		{
			for (int j = 1; j <= n; j++)
			{
				if (odl[i][j] > maksodl[i].second)
				{
					maksodl[i].first = j;
					maksodl[i].second = odl[i][j];
				}
			}
		}
		for (int i = 1; i <= n; i++)
		{
			for (int j = 1; j <= n; j++)
			{
				for (int k = 0; k <= n + 1; k++)
				{
					maksss[i][j][k] = -1;
				}
			}
		}
		for (int i = 1; i <= n; i++)
		{
			for (int j = 1; j <= n; j++)
			{
				for (int k = 1; k <= n; k++)
				{
					maksss[i][j][odl[k][i]] = max(maksss[i][j][odl[k][i]], odl[k][j]);
				}
				for (int k = n; k >= 0; k--)
				{
					maksss[i][j][k] = max(maksss[i][j][k], maksss[i][j][k + 1]);
				}
			}
		}
		//cout << spr(1) << endl;
		int l = 1, r = n - 1;
		while (l <= r)
		{
			int sr = l + (r - l) / 2;
			if (spr(sr))
			{
				r = sr - 1;
				odpo = sr;
			}
			else
			{
				l = sr + 1;
			}
		}
		cout << odpo << endl;
	}
	return 0;
}