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#include <bits/stdc++.h>

using namespace std;

typedef unsigned uint;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ldbl;
typedef pair<int, int> pii;
typedef pair<uint, uint> puu;
typedef pair<ll, ll> pll;
typedef pair<ull, ull> pull;
typedef pair<double, double> pdd;
typedef vector<int> vi;
typedef vector<uint> vu;
typedef vector<ll> vll;
typedef vector<ull> vull;
typedef vector<pii> vpii;
typedef vector<puu> vpuu;
typedef vector<pll> vpll;
typedef vector<pull> vpull;
typedef vector<string> vstr;
typedef vector<double> vdbl;
typedef vector<ldbl> vldbl;
#define pb push_back
#define ppb pop_back
#define pfr push_front
#define ppfr pop_front
#define emp emplace
#define empb emplace_back
#define be begin
#define rbe rbegin
#define all(x) (x).be(), (x).end()
#define rall(x) (x).rbe(), (x).rend()
#define fir first
#define sec second
#define mkp make_pair
#define brif(cond) if (cond) break
#define ctif(cond) if (cond) continue
#define retif(cond) if (cond) return
void fastio() {ios_base::sync_with_stdio(false);cin.tie(nullptr);}
template<typename T> T gcd(T a, T b) {return b ? gcd(b, a%b) : a;}
template<typename T> T extgcd(T a, T b, T &x, T &y)
{
    T x0 = 1, y0 = 0, x1 = 0, y1 = 1;
    while (b) {
        T q = a/b; a %= b; swap(a, b);
        x0 -= q*x1; swap(x0, x1);
        y0 -= q*y1; swap(y0, y1);
    }
    x = x0; y = y0; return a;
}
int ctz(uint x) {return __builtin_ctz(x);}
int ctzll(ull x) {return __builtin_ctzll(x);}
int clz(uint x) {return __builtin_clz(x);}
int clzll(ull x) {return __builtin_clzll(x);}
int popcnt(uint x) {return __builtin_popcount(x);}
int popcntll(ull x) {return __builtin_popcountll(x);}
int bsr(uint x) {return 31^clz(x);}
int bsrll(ull x) {return 63^clzll(x);}

struct P {
    int x, y, d;
};

bool cmp(const  P &lhs, const P &rhs) { return lhs.d > rhs.d; }

#define N 400

char a[N][N];
int d[N][N];
P ps[N*(N-1)/2];

void solve()
{
    int n, m = 0;
    int ans = N;

    cin >> n;
    for (int i = 0; i < n; ++i) {
        cin >> a[i];
        for (int j = 0; j < n; ++j) d[i][j] = a[i][j] == '1' ? 1 : N;
        d[i][i] = 0;
    }
    for (int k = 0; k < n; ++k) {
        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < n; ++j) d[i][j] = min(d[i][j], d[k][i]+d[k][j]);
        }
    }

    for (int i = 0; i < n; ++i) {
        for (int j = i+1; j < n; ++j) ps[m++] = {i, j, d[i][j]};
    }
    sort(ps, ps+m, cmp);
    //int opc = 0; cerr << "init = " << ps[0].d << '\n';

    for (int i = 0; i < m; ++i) {
        int x = ps[i].x;
        int y = ps[i].y;
        int dmax = 0;
        for (int j = 0; j < m && dmax < ans; ++j) {
            //++opc;
            brif(ps[j].d <= dmax);
            int u = ps[j].x;
            int v = ps[j].y;
            int duv = min(d[x][u]+d[y][v], d[x][v]+d[y][u]);
            dmax = max(dmax, duv);
        }
        ans = min(ans, dmax);
        //cerr << x << ", " << y << " -> " << dmax << '\n';
    }
    //cerr << opc << " ops\n";
    cout << ans << '\n';
}

int main()
{
    fastio();

    int t;
    cin >> t;
    for (; t; --t) solve();

    return 0;
}