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#include <cstdio>
#include <cstdint>
#include <vector>
#include <bitset>
#include <cmath>
#include <iostream>
#include <climits>

using namespace std;

const int MAXN = 400;
const int THEMAX = 10000;

vector<vector<short>> A(MAXN+5, vector<short>(MAXN+5));
vector<vector<short>> Working(MAXN+5, vector<short>(MAXN+5));


int n;

void init()
{
    scanf("%d",&n);
    char currenLine[2*MAXN+5];
    for(int i =0;i<n;++i)
    {
        scanf("%s", currenLine);
        for(int j=0;j<n;++j)
        {
            A[i][j] = (currenLine[j]=='1')?1:THEMAX;
        }
    }
    for(int i =0;i<n;++i)
        A[i][i]=0;
}

void printW()
{
    for(int i = 0;i<n; ++i)
    {
        for(int j = 0; j<n; ++j)
        {
            if(Working[i][j] < THEMAX)
            {
                cout<<Working[i][j];
            }
            else
            {
                cout<<"-";
            }
        }
        cout<<endl;
    }
    cout<<endl;

}

short doFloyd()
{
    for(int j = 0; j<n; ++j)
    for(int i = 0; i<n; ++i)
    for(int k = 0; k<n; ++k)
    {
        short newPath = Working[i][j] + Working[j][k];
        if(newPath < THEMAX)
        {
            Working[i][k] = min(Working[i][k], newPath);
        }
    }

    short theMin = -1;

    for(int i = 0; i<n; ++i)
    for(int j = 0; j<n; ++j)
    {
        short path = Working[i][j];
        if (path < THEMAX && path >= 0)
        {
            theMin = max(theMin, path);
        }
        else
        {
            return THEMAX;
        }
    }
    return theMin;
}

void prepareFloyd(int a, int b)
{
    for(int i = 0;i<n;++i)
    for(int j= 0;j<n;++j)
    {
        Working[i][j] = A[i][j];
    }
    for(int i = 0;i<n;++i)
    {
        Working[i][b] = Working[i][a] = min(A[i][a], A[i][b]);
        Working[b][i] = Working[a][i] = min(A[a][i], A[b][i]);
    }

    Working[a][b]=Working[b][a]=0;

    for(int i = 0;i<n;++i)
        Working[i][i]=0;
}

void calculate()
{
    int theMax = THEMAX;//doFloyd();
    //prepareFloyd(0,4);
    //int temp = doFloyd();
    //cout<<"the result: "<<temp<<endl;
    //printW();
    for(int i = 0; i<n; ++i)
    {
        
        for(int j = i+1; j<n; ++j)
        {
            prepareFloyd(i,j);
            //cout<<"Testing "<<i+1<<" "<<j+1<<endl;
            //printW();
            int currentMin =  doFloyd();
            //cout<<"Flopryd "<<currentMin<<endl;
            theMax = min(theMax, currentMin);
        }
        
    }
    //printW();
    printf("%d\n", theMax);
}


int main ()
{
    int t;
    scanf("%d\n", &t);
    for(int i =0;i<t;++i)
    {
        init();
        calculate();
    }
}