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#include <bits/stdc++.h>
#include <bits/stdc++.h>
#define pb push_back
#define f first
#define s second
#define ll long long
#define dbg(x) cerr << #x << ": " << x << "\n"
#define mp make_pair

using namespace std;

const int N = 405;
const int inf = 1e9;

vector<int> e[N];
vector<pair<int, int>> tab[N];
int dis[N][N];
string input[N];

void solve()
{
    int n;
    cin >> n;

    for (int i = 1; i <= n; i++)
    {
        cin >> input[i];
        e[i].clear();
    }

    for (int i = 1; i <= n; i++)
    {
        for (int j = 1; j <= n; j++)
        {
            if (input[i][j - 1] == '1')
                e[i].pb(j);
        }
    }

    for (int i = 1; i <= n; i++)
    {
        for (int j = 1; j <= n; j++)
            dis[i][j] = inf;
        queue<int> Q;
        Q.push(i);
        dis[i][i] = 0;

        while (!Q.empty())
        {
            int u = Q.front();
            Q.pop();
            for (int v : e[u])
            {
                if (dis[i][v] == inf)
                {
                    Q.push(v);
                    dis[i][v] = dis[i][u] + 1;
                    tab[i].pb({dis[i][v], v});
                }
            }
        }
        sort(tab[i].begin(), tab[i].end());
        reverse(tab[i].begin(), tab[i].end());
    }

    int res = inf;

    for (int tel_i = 1; tel_i <= n; tel_i++)
    {
        // cout << tel_i << "\n";
        for (int tel_j = tel_i + 1; tel_j <= n; tel_j++)
        {
            int tel_res = 0;
            for (int i = 1; i <= n; i++)
            {
                for (auto [len, j] : tab[i])
                {
                    if (j <= i)
                        continue;
                    int mini = min(dis[i][tel_i] + dis[tel_j][j], dis[i][tel_j] + dis[tel_i][j]);
                    tel_res = max(tel_res, min(dis[i][j], mini));
                    if (dis[i][j] <= mini)
                        break;
                }
            }
            // cout << tel_j << " " << tel_res << "\n";
            res = min(res, tel_res);
        }
    }

    cout << res << "\n";
}

int main()
{
    cin.tie(0)->sync_with_stdio(0);

    int t;
    cin >> t;

    while (t--)
        solve();

    return 0;
}