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#include <bits/stdc++.h>
using namespace std;
typedef pair<int,int> PII;

const int N = 405;
int G[N][N];
int dist[N][N];
vector<PII> distp[N];

struct Edge{
    int a, b, val;
};

void solve() {
    int n;
    cin>>n;

    for(int i=0;i<n;i++) for(int j=0;j<n;j++) if(i != j) dist[i][j] = 1e9;
    for(int i=0;i<=n;i++) distp[i].clear();

    for(int i=0;i<n;i++) {
        for(int j=0;j<n;j++) {
            char x;
            cin>>x;
            if(x == '1') G[i][j] = 1, dist[i][j] = 1;
            else G[i][j] = 0;
        }
    }

    for(int k=0;k<n;k++) {
        for(int i=0;i<n;i++) {
            for(int j=0;j<n;j++) {
                dist[i][j] = min(dist[i][j], dist[i][k] + dist[k][j]);
            }
        }
    }

    vector<Edge> okp;
    for(int i=0;i<n;i++) {
        for(int j=i+1;j<n;j++) {
            okp.push_back({i, j, 0});
            distp[dist[i][j]].push_back({i, j});
        }
    }

    mt19937 gen(2137);
    for(int i=1;i<=n;i++) shuffle(distp[i].begin(), distp[i].end(), gen);

    vector<Edge> tmp;
    int res = 0;
    for(int d=n;d>0;d--) {
        for(Edge e: okp) if(e.val < d) tmp.push_back(e);
        swap(okp, tmp);
        tmp.clear();
        if(okp.empty()) {
            cout<<d<<endl;
            return;
        }

        for(auto [a, b]: distp[d]) {
            for(Edge e: okp) {
                int new_val = min(dist[e.a][a] + dist[e.b][b], dist[e.a][b] + dist[e.b][a]);
                if(new_val < d) {
                    e.val = max(e.val, new_val);
                    tmp.push_back(e);
                }
            }
            swap(okp, tmp);
            tmp.clear();
            if(okp.empty()) {
                cout<<d<<endl;
                return;
            }
        }
    }
}

int main() {
    ios_base::sync_with_stdio(0);
    int Z;
    cin>>Z;
    while(Z--) solve();
}