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#include <vector>
#include <cstdio>
#include <stack>
#include <algorithm>
#include <queue>
#include <map>
#include <cmath>
#include <unordered_set>
#include <unordered_map>
#include <set>
#include <cstring>
#include <bitset>
#include <iostream>
#include <queue>
#include <iomanip>
#include <complex>
#include <numeric>
#include <random>

using namespace std;

#define ALL(x) x.begin(), x.end()
#define UNIQUE(c) (c).resize(unique(ALL(c)) - (c).begin())
#define FOR(i, a, b) for(int i =(a); i <=(b); ++i)
#define RE(i, n) FOR(i, 1, n)
#define RED(i, n) FORD(i, n, 1)
#define FORD(i, a, b) for(int i = (a); i >= (b); --i)
#define REP(i, n) for(int i = 0;i <(n); ++i)
#define REPD(i, n) FORD(i, n-1,0)

#define printA(a, L, R) FOR(i,L,R) cout << a[i] << (i==R?'\n':' ')
#define printV(a) printA(a,0,a.size()-1)
#define PRESENT(c, x) ((c).find(x) != (c).end())
#define CPRESENT(c, x) (find(ALL(c),x) != (c).end())
#define bit(x, i) (x&(1<<i))
#define lowbit(x) ((x)&((x)^((x)-1)))

const int fx[4][2] = {
    {0, 1},
    {0, -1},
    {1, 0},
    {-1, 0}
};
const int fxx[8][2] = {
    {0, 1},
    {0, -1},
    {1, 0},
    {-1, 0},
    {1, 1},
    {1, -1},
    {-1, 1},
    {-1, -1}
};
const int sk[8][2] = {
    {2, 1},
    {2, -1},
    {-2, -1},
    {-2, 1},
    {1, 2},
    {-1, 2},
    {1, -2},
    {-1, -2}
};

const int maxn = 410;
long long mod = 998244353ll;
const long long inf = 10000000000012ll;
int n, odl[maxn][maxn], res;
string s;

void solve() {
    cin >> n;
    RE(i, n) {
        cin >> s;
        RE(j, n)if (i != j)odl[i][j] = s[j - 1] == '0' ? maxn : 1;
    }
    res = maxn;
    RE(k, n)
        RE(i, n)
            RE(j, n) odl[i][j] = min(odl[i][j], odl[i][k] + odl[k][j]);

    vector<tuple<int, int, int> > v;
    RE(i, n)
        FOR(j, i + 1, n)v.emplace_back(-odl[i][j], i, j);
    sort(ALL(v));
    vector<int> vec(n);
    iota(vec.begin(), vec.end(), 1);
    shuffle(ALL(vec), default_random_engine(42));
    REP(i, n)
        FOR(j, i + 1, n - 1) {
            int nres = 0;
            for (auto &[o, a, b]: v) {
                nres = max(nres, min(-o, min(odl[a][vec[i]] + odl[vec[j]][b], odl[b][vec[i]] + odl[vec[j]][a])));
                if (nres >= res)break;
            }
            res = min(res, nres);
        }
    cout << res << "\n";
}

int main() {
    ios_base::sync_with_stdio(false), cin.tie(nullptr);

    int tt = 1;
    cin >> tt;
    while (tt--) {
        solve();
    }
    return 0;
}