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#include <cstdio>
#include <algorithm>
#include <vector>
#include <ctime>
#include <cmath>
using namespace std;

const int MAX_SIZE = 402;
const int INF = 100000;
const int BRUT_THRESHOLD = 200;

char adj[MAX_SIZE][MAX_SIZE];
int dist[MAX_SIZE][MAX_SIZE];
int perm[MAX_SIZE];
vector<pair<int,int>> paths_of_length[MAX_SIZE];
vector<int> firsts[MAX_SIZE];
vector<int> seconds[MAX_SIZE];

inline int turboMin(int a, int b) { 
	return b + ((a-b) & (a-b)>>31);
}

inline int turboMax(int a, int b) { 
	return a - ((a-b) & (a-b)>>31);
}

void calcDist(int n) {
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            if (i == j) {
                dist[i][j] = 0;
            } else if (adj[i][j] == '1') {
                dist[i][j] = 1;
            } else {
                dist[i][j] = INF;
            }
        }
    }
    for (int k = 0; k < n; k++) {
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (dist[i][j] > dist[i][k] + dist[k][j]) { 
                    dist[i][j] = dist[i][k] + dist[k][j];
                }
            }
        }
    }
    for (int i = 0; i <= n; i++) {
        paths_of_length[i].clear();
    }
    for (int i = 0; i < n; i++) {
        for (int j = i + 1; j < n; j++) {
            paths_of_length[dist[i][j]].emplace_back(i, j);
        }
    }
    for (int i = 0; i <= n; i++) {
        random_shuffle(paths_of_length[i].begin(), paths_of_length[i].end());
    }
    for (int i = 0; i <= n; i++) {
        firsts[i].resize(paths_of_length[i].size());
        seconds[i].resize(paths_of_length[i].size());
        for (size_t j = 0; j < paths_of_length[i].size(); j++) {
            firsts[i][j] = paths_of_length[i][j].first;
            seconds[i][j] = paths_of_length[i][j].second;
        }
    }
}

int best_for_2(int n, int a, int b, int curBest) {
    int maxTeleLen = 0;
    int best = INF;

    auto& distA = dist[a];
    auto& distB = dist[b];

    for (int G = n; G > 0; G--) {
        size_t limit = firsts[G].size();
        const vector<int>& f = firsts[G];
        const vector<int>& s = seconds[G];
        for (size_t idx = 0; idx < limit; ++idx) {
            int w1 = f[idx];
            int w2 = s[idx];
            int dAw1 = distA[w1];
            int dBw1 = distB[w1];
            int dAw2 = distA[w2];
            int dBw2 = distB[w2];
            int pl = turboMin(dAw1, dBw1) + turboMin(dAw2, dBw2);
            if (pl > maxTeleLen) {
                maxTeleLen = pl;
                if (maxTeleLen >= curBest) {
                    return best;
                }
            }
        }
        if (maxTeleLen >= best) {
            return best;
        }
        best = max(maxTeleLen, G - 1);
    }
    return maxTeleLen;
}

int judge(int n, int a, int b) {
    int mx = 0;
    for (int i = 0; i < n; i++) {
        for (int j = i + 1; j < n ; j++) {
            mx = max(mx, 
                min(
                    dist[i][j],
                    min(dist[a][i], dist[b][i]) + min(dist[a][j], dist[b][j])));
        }
    }
    return mx;
}

pair<int, int> proposeNear(int n, int a, int b) {
    vector<pair<int, int>> props;
    for (int i = 0; i < n; i++) {
        if (dist[i][a] == 1) {
            props.emplace_back(i, b);
        }
        if (dist[i][b] == 1) {
            props.emplace_back(a, i);
        }
    }
    return props[rand() % props.size()];
}

int anneal(int n) {
    int global_min = n;
    for (int k = 0; k < 4; k++) {
        float T = 1;
        float T_min = 0.003;
        float alpha = 0.9;
        int numIterations = 100;

        int a = rand() % n;
        int b = rand() % n;
        int sol_val = judge(n, a, b);
        global_min = min(global_min, sol_val);

        while (T > T_min) {
            for (int iter = 0; iter < numIterations; iter++) {
                if (sol_val < global_min) {
                    global_min = sol_val;
                }
                pair<int, int> next = proposeNear(n, a, b);
                int prop_a = next.first;
                int prop_b = next.second;
                int new_min = judge(n, prop_a, prop_b);
                float acceptProbab = exp((sol_val - new_min) / T);
                if (acceptProbab > (float) rand() / RAND_MAX) {
                    a = prop_a;
                    b = prop_b;
                    sol_val = new_min;
                }
            }
            T *= alpha; 

            //printf("TEMP %f, wyn %d\n", T, global_min);
        }
    }

    return global_min;
}

int brutuj(int n) {
    int wyn = n;
    for (int i = 0; i < n; i++) {
        perm[i] = i;
    }
    random_shuffle(perm, perm + n);
    for (int i = 0; i < n; i++) {
        random_shuffle(perm + i + 1, perm + n);
        for (int j = i + 1; j < n; j++) {
            wyn = min(wyn, best_for_2(n, perm[i], perm[j], wyn));
        }
    }
    return wyn;
}

int runSingleTest() {
    int n;
    scanf("%d", &n);
    for (int i = 0; i < n; i++) {
        scanf("%s", adj[i]);
    }
    calcDist(n);
    int wyn = n <= BRUT_THRESHOLD ? brutuj(n) : anneal(n);
    return wyn;
}

int main() {
    srand(time(NULL));
    int T;
    scanf("%d", &T);
    for (int i = 0; i < T; i++) {
        int res = runSingleTest();
        printf("%d\n", res);
    }
}