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#include <bits/stdc++.h>

using namespace std;

#ifdef LOCAL
#include "debug.h"
#define dassert assert
#define debug(...) {}
#define dassert(...) {}
#else
#define debug(...) {}
#define dassert(...) {}
#endif

#define x first
#define y second
#define ir(a, x, b) ((a) <= (x) && (x) <= (b))
#define vec vector
#define rep(i, a, b) for (int i = a; i < (b); ++i)
#define all(x) (x).begin(), (x).end()
#define sz(x) ((ll)((x).size()))

using ll = long long;
using bt = bitset<401>;

struct matrix {
    int n;
    vec<bt> t;
    matrix(int n_) : n(n_), t(n) {}

    friend void operator |=(matrix& a, const matrix& b) {
        dassert(a.t.size() == b.t.size());
        rep (i, 0, sz(a.t)) {
            a.t[i] |= b.t[i];
        }
    }

    bt& operator [](int i) {
        return this->t[i];
    }

    friend bool full(const matrix& m) {
        for (auto b : m.t) {
            if ((ll)b.count() != m.n) {
                return false;
            }
        }
        return true;
    }
};

int d[410][410];

vec<vec<int>> ord;
vec<vec<bt>> mask;

void get(matrix &m, int N, int a, int b, int md) {
    rep (j, 0, N) {
        int v = ord[a][j];
        // v--a-T-b--u, ensure dist <= md
        if (d[a][v] > md) break;
        int max_d_from_b = md - d[a][v];
        dassert(max_d_from_b >= 0);
        bt& msk = mask[b][min((int)sz(mask[b])-1, max_d_from_b)];
        m[v] |= msk;
    }
}

// string getout() {
// #define cout stream
//     stringstream stream;
//     stream << "1\n";
//     int N = 400;
//     stream << N << "\n";
//     rep (a, 0, N) {
//         rep (b, 0, N) {
//             if (a == ((b+1)%N)) stream << "1";
//             else if (b == ((a+1)%N)) stream << "1";
//             else stream << "0";
//         }
//         stream << "\n";
//     }
//     return stream.str();
// #undef cout
// }
//
// string getout1() {
// #define cout stream
//     stringstream stream;
//     int x = 133;
//     int N = 3*x+1;
//     vec g(N, vec(N, false));
//     rep (a, 0, 3) {
//         int prev = 0;
//         rep (b, 0, x) {   
//             int v = 1 + a*x + b;
//             g[v][prev] = g[prev][v] = 1;
//             prev = v;
//         }
//     }
//     stream << "1\n";
//     stream << g.size() << "\n";
//     for (auto &x : g) {
//         for (auto v : x) {
//             cout << v;
//         }
//         cout << "\n";
//     }
//     return stream.str();
// #undef cout
// }
//
// // #define TESTRUN
// #ifdef TESTRUN
// #define cin stream
// istringstream stream(getout1());
// #endif
//
void solve() {
    int N; cin >> N;
    // TODO: clear all globals
    // TODO: calc memory
    rep (n, 0, N) {
        string s; cin >> s;
        rep (k, 0, N) {
            if (s[k] == '1') d[n][k] = d[k][n] = 1;
            else d[n][k] = d[k][n] = int(1e9);
        }
    }

    rep (i, 0, N) d[i][i] = 0;
    rep (j, 0, N) rep (i, 0, N) rep (k, 0, N) {
        d[i][k] = min(d[i][k], d[i][j] + d[j][k]);
    }

    ord.clear();
    mask.clear();
    ord = vec<vec<int>>(N, vec<int>(N));
    mask = vec<vec<bt>>(N);
    rep (a, 0, N) {
        iota(all(ord[a]), 0);
        sort(all(ord[a]), [&](int v, int u) {
            return d[a][v] < d[a][u];
        });

        int v = a;
        mask[v].emplace_back();
        mask[v][0][v] = 1;
        int cd = 1;
        int i = 1;
        debug(mask[v].size());
        while (mask[v].back().count() != N) {
            // debug(cd, mask[v].back(), N);
            mask[v].push_back(mask[v].back());
            while (i < N && d[v][ord[v][i]] <= cd) {
                mask[v].back()[ord[v][i]] = 1;
                i++;
            }
            cd++;
        }
    }

    vec<pair<int, int>> idcs;
    rep (a, 0, N) rep (b, 0, a) idcs.push_back({a, b});

    int idx = 0;
    int cd = N;
    int best = 1e9;

    int currentd = -1;
    matrix dd(N);

    while (idx < sz(idcs) && cd >= 0) {
        auto [a, b] = idcs[idx];
        if (currentd != cd) {
            currentd = cd;
            dd = matrix(N);
            rep (v, 0, N) rep (u, 0, N) {
                if (d[v][u] <= cd) {
                    dd[v][u] = 1;
                    dd[u][v] = 1;
                }
            }
        }

        matrix m = dd;
        get(m, N, a, b, cd);
        get(m, N, b, a, cd);
        if (full(m)) {
            debug(a, b, cd);
            best = cd;
            cd--;
        } else {
            idx++;
        }
    }
    cout << best << endl;
}

int main() {
    cin.tie(0)->sync_with_stdio(0);
    int T; cin >> T;
    while (T--) solve();
    return 0;
}