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#include <bits/stdc++.h>
#define ull unsigned long long
#define pb push_back
#define pf push_front
#define in insert
#define f first
#define s second
#define pii pair<int, int>
#define pib pair<int, bool>
#define cint const int
#define mn2 262144
#define nw '\n'
#define sp " "
using namespace std;
const int inf = 1e9;
vector<vector<int>> diameter(int n, const vector<vector<int>>& pol) {
    vector<vector<int>> dist(n+1, vector<int>(n+1, inf));
    for (int u=1; u<=n; ++u) {
        queue<int> q;
        q.push(u);
        dist[u][u]=0;
        while (!q.empty()) {
            int v=q.front();
            q.pop();
            for (int it:pol[v]) {
                if (dist[u][it]>dist[u][v]+1) {
                    dist[u][it]=dist[u][v]+1;
                    q.push(it);
                }
            }
        }
    }
    return dist;
}

int main() {
    ios_base::sync_with_stdio(0); cin.tie(0);
    int t;
    cin>>t;
    while (t--) {
        int n;
        cin>>n;
        vector<vector<int>> pol(n+1);
        for (int u=1; u<=n; ++u) {
            string su;
            cin>>su;
            for(int v=1; v<=n; ++v) if (su[v-1]=='1') pol[u].push_back(v);
        }
        auto dist=diameter(n, pol);
        int odp=0;
        for (int u=1; u<=n; ++u) for(int v=1; v<=n; ++v) if(dist[u][v]!=inf) odp=max(odp, dist[u][v]);
        int wyn=odp;
        for (int u=1; u<=n; ++u) {
            for (int v=u+1; v<=n; ++v) {
                int tmp=0;
                for (int a=1; a<=n; ++a) {
                    for (int b=1; b<=n; ++b) {
                        int d=min({dist[a][b], dist[a][u]+dist[v][b], dist[a][v]+dist[u][b]});
                        tmp=max(tmp, d);
                    }
                }
                wyn=min(wyn, tmp);
            }
        }
        cout<<wyn<<nw;
    }
    return 0;
}