#include<cstdio>

 #include<time.h>

 #include<cstring>

 #include<iostream>

 #include<algorithm>

 using namespace std;

 const int maxn = <<;

 int num1[maxn+];

 int que[];

 void dabiao()

 {

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

     {

         int t = ;

         for(int j = ;j < ;++j)

         if(i & ( << j)) t++;

         num1[i] = t;

     }

 }

 int main()

 {

     dabiao();

     int T,n;

     scanf("%d",&T);

     while(T--)

     {

         scanf("%d",&n);

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

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

         int ans = 0x7fffffff,suiji = ;

         srand( (unsigned)time( NULL ) );  //不加种子就过不了

         while(suiji--)

         {

             int r1 = rand() % n;

             int r2 = rand() % n;

             if(r1 != r2)

             ans = min(ans,num1[que[r1]^que[r2]]);

         }

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

     }

     return ;

 }