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#include <bits/stdc++.h>


using namespace std;


bool check(int d, int n, vector <vector<int>> &dist) {
    int numFarPairs = 0;
    for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) {
        numFarPairs += dist[i][j] > d;
    }

    vector <vector<int>> coveredFarPairs(n, vector <int> (n, 0));

    vector <int> atDist(d + 1, 0);
    for (int jTel = 0; jTel < n; jTel++) for (int i = 0; i < n; i++) {
        for (int x = 0; x <= d; x++) {
            atDist[x] = 0;
        }

        for (int j = 0; j < n; j++) if (dist[i][j] > d && dist[jTel][j] <= d) {
            atDist[dist[jTel][j]]++;
        }

        for (int x = 1; x <= d; x++) {
            atDist[x] += atDist[x - 1];
        }

        if (atDist[d] == 0) {
            continue;
        }

        int iTel = 0;
        while (iTel + 4 <= n) {
            int dLeft1 = d - dist[i][iTel];
            int dLeft2 = d - dist[i][iTel + 1];
            int dLeft3 = d - dist[i][iTel + 2];
            int dLeft4 = d - dist[i][iTel + 3];

            if (dLeft1 >= 0) coveredFarPairs[jTel][iTel] += atDist[dLeft1];
            if (dLeft2 >= 0) coveredFarPairs[jTel][iTel + 1] += atDist[dLeft2];
            if (dLeft3 >= 0) coveredFarPairs[jTel][iTel + 2] += atDist[dLeft3];
            if (dLeft4 >= 0) coveredFarPairs[jTel][iTel + 3] += atDist[dLeft4];

            iTel += 4;
        }

        while (iTel < n) {
            int dLeft = d - dist[i][iTel];
            if (dLeft >= 0) coveredFarPairs[jTel][iTel] += atDist[dLeft];

            iTel++;
        }
    }

    for (int iTel = 0; iTel < n; iTel++) for (int jTel = iTel + 1; jTel < n; jTel++) {
        int covered = coveredFarPairs[iTel][jTel] + coveredFarPairs[jTel][iTel];
        if (covered == numFarPairs) {
            return true;
        }
    }

    return false;
}

int solve(int n, vector <vector<int>> &g) {
    vector <vector<int>> dist(n, vector <int> (n, n));

    for (int i = 0; i < n; i++) {
        dist[i][i] = 0;
    }

    for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) if (g[i][j]) {
        dist[i][j] = 1;
    }

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

    int maxDist = 0;
    for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) {
        maxDist = max(maxDist, dist[i][j]);
    }

    int l = 0, r = maxDist;
    while (r - l > 1) {
        int mid = (l + r) / 2;
        if (check(mid, n, dist)) {
            r = mid;
        } else {
            l = mid;
        }
    }

    return r;
}

int main() {
    ios_base::sync_with_stdio(false);

    int t;
    cin >> t;

    while (t--) {
        int n;
        cin >> n;

        vector <vector<int>> g(n, vector <int> (n));
        for (int i = 0; i < n; i++) {
            string s;
            cin >> s;

            for (int j = 0; j < n; j++) {
                g[i][j] = s[j] == '1';
            }
        }

        cout << solve(n, g) << '\n';
    }

    return 0;
}