#include <stdio.h>

 #include <algorithm>

 #include <time.h>

 #include <math.h>

 using namespace std;

 const int N=;

 const int INF=<<;

 int f[N];

 int main()

 {

     int t;

     scanf("%d",&t);

     while(t--)

     {

         int n,ans = INF;

         scanf("%d",&n);

         for (int i = ; i < n; i ++)

             scanf("%x",&f[i]);

         srand((unsigned)time(NULL));

         for (int i = ; i < N*; i ++)

         {

             int a = rand()%n;

             int b = rand()%n;

             if (a==b)

                 continue ;

             int t = f[a]^f[b];

             int temp = __builtin_popcount(t);

             ans = min(ans,temp);

         }

         printf("%d\n",ans);

     }

     return ;

 }