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#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

#ifdef LOCAL
#include "../debug/debug.h"
#else
#define debug(...)
#define debugArr(...)
#endif

using namespace std;
using namespace __gnu_pbds;

using ll = long long;
using db = long double;
using pi = pair<int,int>;
using pl = pair<ll,ll>;
using vi = vector<int>;
using vl = vector<ll>;
using vb = vector<bool>;
using vpi = vector<pi>;
using vpl = vector<pl>;
using vvi = vector<vi>;

#define mp make_pair
#define eb emplace_back
#define pb push_back
#define x first
#define y second
#define sz(x) int((x).size())
#define bg(x) begin(x)
#define all(x) (x).begin(),(x).end()
#define rall(x) (x).rbegin(), (x).rend() 
#define rep(i,a,b) for(int i=(a);i<(b);i++)
#define per(i,a,b) for(int i=(b)-1;i>=(a);i--)
#define ft front()
#define bk back()
#define rsz resize
#define ins insert
#define each(a,x) for(auto&a:x)

template<class T> bool ckmin(T& a, T b) { return b<a?a=b,1:0; }
template<class T> bool ckmax(T& a, T b) { return b>a?a=b,1:0; }
template<class T> int lwb(vector<T>& a, const T& b) { return int(lower_bound(all(a),b)-bg(a)); }
template<class T> int upb(vector<T>& a, const T& b) { return int(upper_bound(all(a),b)-bg(a)); }
template<class T> void remdup(vector<T>& v) { sort(all(v)); v.erase(unique(all(v)),end(v)); }

constexpr int pct(int x) { return __builtin_popcount(x); }
constexpr int bitlog(int x) { return x == 0 ? 0 : 31 - __builtin_clz(x); }
constexpr int pct(ll x) { return __builtin_popcountll(x); }
constexpr int bitlog(ll x) { return x == 0 ? 0 : 63 - __builtin_clzll(x); }

constexpr ll cdiv(ll a, ll b) { return a / b + ((a ^ b) > 0 && a % b); }  // divide a by b rounded up
constexpr ll fdiv(ll a, ll b) { return a / b - ((a ^ b) < 0 && a % b); }  // divide a by b rounded down
constexpr int cdiv(int a, int b) { return a / b + ((a ^ b) > 0 && a % b); }  // divide a by b rounded down
constexpr int fdiv(int a, int b) { return a / b - ((a ^ b) < 0 && a % b); }  // divide a by b rounded down

const pi MOVES[] = {{-1, 0}, {0, -1}, {1, 0}, {0, 1}};

#ifdef LOCAL
mt19937_64 rng(0xabadbeef);
#else
mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
#endif

ll randr(ll l, ll r) { return uniform_int_distribution<ll>(l, r)(rng); }

const int N = 408;
const int INF = 1e8;
int d[N][N];
pi dp[N][N][2];
string s[N];
int n;

void upd(pi* a, int i, int dist) {
    pi cur(dist, i);
    if (ckmax(a[1], cur)) {
        if (a[1] > a[0]) swap(a[1], a[0]);
    }
}

bool maybe(int dist) {
    rep(a,0,n) {
        rep(x,0,n) {
            dp[a][x][0] = dp[a][x][1] = make_pair(0, -1);
        }
    }

    rep(a,0,n) {
        rep(b,0,n) {
            if (d[a][b] <= dist) continue;
            rep(x,0,n) {
                if (x == b) continue;
                upd(dp[a][x], b, d[b][x]);
            }
        }
    }

    rep(x,0,n) {
        rep(y,x+1,n) {
            bool ok = true;
            rep(a,0,n) {
                if (a == x || a == y) continue;
                if (d[a][x] <= d[a][y]) {
                    auto [d1, b1] = dp[a][y][0];
                    auto [d2, b2] = dp[a][y][1];

                    if (b1 == x) {
                        if (d[a][x] + d2 > dist) {
                            ok = false;
                            break;
                        }
                    }
                    else {
                        if (d[a][x] + d1 > dist) {
                            ok = false;
                            break;
                        }
                    }
                }
                else {
                    auto [d1, b1] = dp[a][x][0];
                    auto [d2, b2] = dp[a][x][1];

                    if (b1 == y) {
                        if (d[a][y] + d2 > dist) {
                            ok = false;
                            break;
                        }
                    }
                    else {
                        if (d[a][y] + d1 > dist) {
                            ok = false;
                            break;
                        }
                    }
                }
            }

            if (ok) {
                return true;
            }
        }
    }

    return false;
}

void solve() {
    cin >> n;
    rep(i,0,n) {
        rep(j,0,n) d[i][j] = INF;
    }

    rep(i,0,n) d[i][i] = 0;

    rep(i,0,n) {
        cin >> s[i];
        rep(j,0,n) {
            if (s[i][j] == '1') {
                d[i][j] = 1;
            }
        }
    }

    rep(k,0,n) {
        rep(i,0,n) {
            rep(j,0,n) {
                ckmin(d[i][j], d[i][k] + d[k][j]);
            }
        }
    }

    int res = 1;
    rep(a,0,n) {
        rep(b,a+1,n) {
            ckmax(res, d[a][b]);
        }
    }

    int l = 1;
    int r = res;
    while (l <= r) {
        int mid = (l + r) / 2;
        if (maybe(mid)) {
            res = mid;
            r = mid - 1;
        }
        else {
            l = mid + 1;
        }
    }

    cout << res << '\n';
}

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

    int t;
    cin >> t;
    while (t--) {
        solve();
    }

    return 0;
}