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#include <iostream>
#include <vector>
#include <queue>
#include <algorithm>

using namespace std;

const int INF = 1e9;

int graph_diameter(const vector<vector<int>> &dist, int n) {
    int diameter = 0;
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            if (dist[i][j] < INF) {
                diameter = max(diameter, dist[i][j]);
            }
        }
    }
    return diameter;
}

void floyd_warshall(vector<vector<int>> &dist, int n) {
    for (int k = 0; k < n; k++) {
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                dist[i][j] = min(dist[i][j], dist[i][k] + dist[k][j]);
            }
        }
    }
}

int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    
    int t;
    cin >> t;
    
    while (t--) {
        int n;
        cin >> n;
        
        vector<vector<int>> adj_matrix(n, vector<int>(n));
        vector<vector<int>> dist(n, vector<int>(n, INF));
        
        for (int i = 0; i < n; i++) {
            string s;
            cin >> s;
            for (int j = 0; j < n; j++) {
                adj_matrix[i][j] = s[j] - '0';
                if (adj_matrix[i][j] == 1) {
                    dist[i][j] = 1;
                }
            }
            dist[i][i] = 0;
        }
        
        floyd_warshall(dist, n);
        
        int original_diameter = graph_diameter(dist, n);
        int min_diameter = original_diameter;
        

        for (int u = 0; u < n; u++) {
            for (int v = u + 1; v < n; v++) {
                vector<vector<int>> new_dist = dist;
                
                for (int i = 0; i < n; i++) {
                    for (int j = 0; j < n; j++) {
                        new_dist[i][j] = min(new_dist[i][j], new_dist[i][u] + new_dist[v][j]);
                        new_dist[i][j] = min(new_dist[i][j], new_dist[i][v] + new_dist[u][j]);
                    }
                }
                
                min_diameter = min(min_diameter, graph_diameter(new_dist, n));
            }
        }
        
        cout << min_diameter << "\n";
    }
    
    return 0;
}