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

const int MAX = 400;
int N;
bool G[MAX][MAX];
bool H[MAX][MAX];
int d[MAX][MAX];
int color[MAX];


void input(){
	cin >> N;
	string s;
	for(int i = 0; i < N; i++){
		cin >> s;
		for(int j = 0; j < N; j++){
			if(s[j] == '0'){
				G[i][j] = false;
			} else {
				G[i][j] = true;
			}
			d[i][j] = -1;
		}
	}
}

// here we use the assumption that the graph is connected!
void find_distances(){
	for(int i = 0; i < N; i++){
		queue<pair<int, int> > Q;
		Q.push(make_pair(i, 0));
		while(!Q.empty()){
			int x = Q.front().first;
			int dix = Q.front().second; 
			Q.pop();

			if(d[i][x] != -1){
				continue;
			}
			d[i][x] = dix;

			for(int j = 0; j < N; j++){
				if(G[x][j]){
					Q.push(make_pair(j, dix + 1));
				}
			}
		}
	}
}

// this little function checks if the graph H is bipartite.
// this is a necessary condition for things to work!
bool is_bipartite(){
	for(int i = 0; i < N; i++){
		color[i] = -1;
	}

	queue<pair<int, int> > Q;
	for(int i = 0; i < N; i++){
		if(color[i] == -1){
			Q.push(make_pair(i, 0));

			while(!Q.empty()){
				int x = Q.front().first;
				int c = Q.front().second;

				Q.pop();

				if(color[x] == -1){
					color[x] = c;

					for(int j = 0; j < N; j++){
						if(H[x][j]){
							Q.push(make_pair(j, 1 - c));
						}
					}
				} else if(color[x] != c){
					return false;
				}
			}
		}
	}

	return true;
}

// this function checks if there exists a pair of vertices
// (x, y) such that x != y and putting a teleport at x and y
// diminishes the distance between any 2 vertices down to 
// at most K.
bool is_valid(int K){
	// all pairs of relevant vertices (a, b) s.t. d(a, b) > K.
	vector<pair<int, int> > V;
	for(int a = 0; a < N; a++){
		H[a][a] = false;
		for(int b = a + 1; b < N; b++){
			if(d[a][b] > K){
				V.push_back(make_pair(a, b));
				H[a][b] = true;
				H[b][a] = true;
			} else {
				H[a][b] = false;
				H[b][a] = false;
			}
		}
	}
	random_shuffle(V.begin(), V.end());
	// if(!is_bipartite()) return false;

	// all pairs (x, y)
	vector<pair<int, int> > all_candidates;
	for(int i = 0; i < N; i++){
		for(int j = i + 1; j < N; j++){
			all_candidates.push_back(make_pair(i, j));
		}
	}
	random_shuffle(all_candidates.begin(), all_candidates.end());

	// the idea is relatively simple:
	// on average, we will reject all candidates rather "quickly"
	for(auto candidate = all_candidates.begin(); candidate != all_candidates.end(); candidate++){
		int x = candidate->first;
		int y = candidate->second;
		bool WORKS = true;
		for(auto v = V.begin(); v != V.end(); v++){
			if(d[v->first][x] + d[y][v->second] > K && d[v->first][y] + d[x][v->second] > K){
				WORKS = false;
				break;
			}
		}
		if(WORKS){
			// found a pair (x, y)!!
			return true;
		}
	}

	// did not find a pair (x, y)
	return false;
}

void find_answer(){
	int max_d = 0;
	for(int i = 0; i < N; i++){
		for(int j = 0; j < N; j++){
			max_d = max(max_d, d[i][j]);
		}
	}

	int a = 1;
	int b = max_d;
	while(a < b){
		int h = (a + b)/2;
		if(is_valid(h)){
			b = h;
		} else {
			a = h + 1;
		}
	}
	cout << a << endl;
}

int main(){
	srand(time(0));
	cin.tie(NULL);
	ios_base::sync_with_stdio(0);
	int T;
	cin >> T;
	for(int v = 0; v < T; v++){
		input();
		find_distances();
		find_answer();
	}
}