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#include <iostream>
#include <cstdio>
#include <vector>
#include <algorithm>
using namespace std;

const int MX = 404;
int T[MX][MX];

void go()
{
    int n;
    cin>>n;
    string s;
    for (int i =0; i<n; i++)
    {
        cin>>s;
        for (int j=0; j<n; j++) if (s[j] == '1') T[i][j]=1;
            else T[i][j] = (i == j ? 0 : 1000);
    }

    int res = 0;

    for (int k=0; k<n; k++)
        for (int i=0; i<n; i++)
            for (int j=0; j<n; j++)
            {
                T[i][j] = min(T[i][j], T[i][k] + T[k][j]);
                if (i!=j)res = max(res, T[i][j]);
            }


    for (int i =0; i<n; i++)
        for (int j=0; j<n; j++)
        {
            int a = 0, b = 0;
            for (int k =0; k<n; k++)
            {
                int c = min(T[k][i], T[k][j]);
                if (c > b)
                {
                    if (c > a)
                    {
                        b = a;
                        a = c;
                    }
                    else
                    {
                        b = c;
                    }
                }
            }
            res = min(res, a + b);
        }

    cout << res << endl;


}

int main()
{
    int t;
    cin>>t;
    while(t--)
    {
        go();
    }

    return 0;
}