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#include <iostream>
#include <vector>
#include <algorithm>
#include <string>
#include <climits>

using namespace std;

int main() {
    int t;
    cin >> t;

    while (t--) {
        int n;
        cin >> n;
        
        // Read the highway connections
        vector<vector<bool>> highways(n, vector<bool>(n, false));
        for (int i = 0; i < n; i++) {
            string s;
            cin >> s;
            for (int j = 0; j < n; j++) {
                highways[i][j] = (s[j] == '1');
            }
        }
        
        // Initialize shortest path distances (Floyd-Warshall)
        vector<vector<int>> dist(n, vector<int>(n, INT_MAX / 2));
        for (int i = 0; i < n; i++) {
            dist[i][i] = 0;
            for (int j = 0; j < n; j++) {
                if (highways[i][j]) {
                    dist[i][j] = 1;
                }
            }
        }
        
        // Floyd-Warshall algorithm to compute shortest paths
        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]);
                }
            }
        }
        
        // Current maximum distance without teleport
        int maxDistance = 0;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                maxDistance = max(maxDistance, dist[i][j]);
            }
        }
        
        // Try all possible teleport placements
        int bestResult = maxDistance;
        
        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                // Create temporary distance matrix with teleport between i and j
                vector<vector<int>> newDist = dist;
                
                // Update distances considering the teleport
                for (int a = 0; a < n; a++) {
                    for (int b = 0; b < n; b++) {
                        // Using teleport from i to j or j to i
                        newDist[a][b] = min(newDist[a][b], 
                                           min(dist[a][i] + dist[j][b], 
                                               dist[a][j] + dist[i][b]));
                    }
                }
                
                // Calculate maximum distance with this teleport
                int currentMax = 0;
                for (int a = 0; a < n; a++) {
                    for (int b = 0; b < n; b++) {
                        currentMax = max(currentMax, newDist[a][b]);
                    }
                }
                
                // Update best result
                bestResult = min(bestResult, currentMax);
            }
        }
        
        cout << bestResult << endl;
    }
    
    return 0;
}