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#include <bits/stdc++.h>

using namespace std;

#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define reunique(v) v.resize(std::unique(v.begin(), v.end()) - v.begin())
#define sz(v) ((int)(v).size())

#define vec1d(x) vector<x>
#define vec2d(x) vector<vec1d(x)>
#define vec3d(x) vector<vec2d(x)>
#define vec4d(x) vector<vec3d(x)>

#define ivec1d(x, n, v) vec1d(x)(n, v)
#define ivec2d(x, n, m, v) vec2d(x)(n, ivec1d(x, m, v))
#define ivec3d(x, n, m, k, v) vec3d(x)(n, ivec2d(x, m, k, v))
#define ivec4d(x, n, m, k, l, v) vec4d(x)(n, ivec3d(x, m, k, l, v))

#define nl "\n"

#ifdef LOCAL
#include "pretty_print.hpp"
#define dbg(...) debug_out(__LINE__, #__VA_ARGS__, __VA_ARGS__)
#else
#define dbg(...) 42
#endif

typedef long double ld;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> pii;

template <typename T> T sqr(T x) { return x * x; }
template <typename T> T abs(T x) { return x < 0? -x : x; }
template <typename T> T gcd(T a, T b) { return b? gcd(b, a % b) : a; }
template <typename T> bool chmin(T &x, const T& y) { if (x > y) { x = y; return true; } return false; }
template <typename T> bool chmax(T &x, const T& y) { if (x < y) { x = y; return true; } return false; }

auto random_address = [] { char *p = new char; return (uint64_t) p; };
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count() * (random_address() | 1));
mt19937_64 rngll(chrono::steady_clock::now().time_since_epoch().count() * (random_address() | 1));


int main(int /* argc */, const char** /* argv */)
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    int t;
    cin >> t;
    while (t--) {
        int n;
        cin >> n;
        auto a = ivec2d(int, n, n, 0);
        auto b = ivec1d(int, n, 0);
        const int inf = 1e9 + 42;
        for (int i = 0; i < n; ++i) {
            string s;
            cin >> s;
            for (int j = 0; j < n; ++j) {
                if (i == j) {
                    a[i][j] = 0;
                } else if (s[j] == '1') {
                    a[i][j] = 1;
                } else {
                    a[i][j] = inf;
                }
            }
        }

        // a = ivec2d(int, n, n, inf);
        // for (int i = 0; i < n; ++i) {
        //     a[i][i] = 0;
        // }
        // for (int i = 0; i + 1 < 100; ++i) {
        //     a[i][i + 1] = 1;
        //     a[i + 1][i] = 1;
        // }
        // for (int i = 0; i < 150; ++i) {
        //     a[0][i + 100] = 1;
        //     a[i + 100][0] = 1;
        //     a[99][i + 250] = 1;
        //     a[i + 250][99] = 1;
        // }

        for (int k = 0; k < n; ++k) {
            for (int i = 0; i < n; ++i) {
                for (int j = 0; j < n; ++j) {
                    chmin(a[i][j], a[i][k] + a[k][j]);
                }
            }
        }
        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < n; ++j) {
                chmax(b[i], a[i][j]);
            }
        }

        int l = 0;
        int r = 0;
        for (int i = 0; i < n; ++i) {
            chmax(r, b[i]);
        }

        vector<int> c1(n);
        iota(all(c1), 0);
        shuffle(all(c1), rng);

        vector<int> c2(n);
        iota(all(c2), 0);
        shuffle(all(c2), rng);

        vector<pii> b12;
        for (int b1 : c1) {
            for (int b2 : c2) {
                if (b1 < b2) {
                    b12.emplace_back(b1, b2);
                }
            }
        }

        while (l < r) {
            int m = (l + r) / 2;
            auto f = ivec1d(int, n, 0);

            bool ok = true;
            queue<int> q;
            auto add = [&](int x, int c) {
                if (f[x]) {
                    if (f[x] != c) {
                        ok = false;
                    }
                    return;
                }
                f[x] = c;
                q.push(x);
            };

            vector<int> w(n, 0);
            for (int i = 0; i < n; ++i) {
                if (f[i] || b[i] <= m) {
                    continue;
                }
                add(i, 1);
                while (!q.empty()) {
                    int x = q.front();
                    q.pop();
                    for (int j = 0; j < n; ++j) {
                        if (a[x][j] > m) {
                            ++w[x];
                            add(j, f[x] ^ 3);
                        }
                    }
                }
            }
            if (!ok) {
                l = m + 1;
                continue;
            }

            vector<int> a1;
            vector<int> a2;
            for (int i = 0; i < n; ++i) {
                if (f[i] == 1) {
                    a1.push_back(i);
                } else if (f[i] == 2) {
                    a2.push_back(i);
                }
            }
            shuffle(all(a1), rng);
            shuffle(all(a2), rng);

            auto check_bases = [&](int b1, int b2) {
                for (int x1 : a1) {
                    for (int x2 : a2) {
                        if (a[x1][x2] <= m) {
                            continue;
                        }
                        if (a[b1][x1] + a[b2][x2] <= m) {
                            continue;
                        }
                        if (a[b1][x2] + a[b2][x1] <= m) {
                            continue;
                        }
                        return false;
                    }
                }
                return true;
            };

            auto found_bases = [&]() {
                for (auto [b1, b2] : b12) {
                    if (check_bases(b1, b2)) {
                        return true;
                    }
                }
                return false;
            };

            ok = found_bases();

            if (ok) {
                r = m;
            } else {
                l = m + 1;
            }
        }
        cout << r << nl;
    }


#ifdef LOCAL
    cerr << "Time execute: " << clock() / (double)CLOCKS_PER_SEC << " sec" << endl;
#endif
    return 0;
}