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#include <bits/stdc++.h>

using namespace std;
#define pb push_back
#define st first
#define nd second
typedef long long ll;
typedef long double ld;
const ll I = 1000'000'000'000'000'000LL;
const int II = 2'000'000'000;
const ll M = 1000'000'007LL;
const int N = 407;
int dis[N][N];
int d2[N][N][N];
vector<pair<int, pair<int, int>>> dv;

void Solve()
{
    int n; string s;
    cin >> n;
    for(int i = 1; i <= n; ++i)
    {
        cin >> s;
        for(int j = 1; j <= n; ++j)
            if(s[j - 1] == '1' || i == j)
                dis[i][j] = 1;
            else
                dis[i][j] = N * 2;
    }
    for(int i = 1; i <= n; ++i)
        for(int j = 1; j <= n; ++j)
            for(int k = 1; k <= n; ++k)
                dis[j][k] = min(dis[j][k], dis[i][j] + dis[i][k]);
    dv.clear();
    for(int i = 1; i <= n; ++i)
        for(int j = i + 1; j <= n; ++j)
            dv.pb(make_pair(dis[i][j], make_pair(i, j)));
    sort(dv.begin(), dv.end());
    reverse(dv.begin(), dv.end());
    for(int i = 1; i <= n; ++i)
        for(int j = i + 1; j <= n; ++j)
            for(int k = 1; k <= n; ++k)
                d2[i][j][k] = min(dis[i][k], dis[j][k]);
    int ans = N;
    for(int i = 1; i <= n; ++i)
        for(int j = i + 1; j <= n; ++j)
        {
            int l = 0, cur = 0;
            while(l < (int)dv.size() && cur < dv[l].st)
            {
                cur = max(cur, min(dv[l].st, d2[i][j][dv[l].nd.st] + d2[i][j][dv[l].nd.nd]));
                ++l;
            }
            ans = min(ans, cur);
        }
    cout << ans << "\n";
}

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    int t; cin >> t;
    while(t--)
        Solve();

    return 0;
}