#pragma comprint(linker, "/STACK:1024000000,1024000000")
#include<cstdio>
#include<string>
#include<iostream>
#include<cstring>
#include<cmath>
#include<stack>
#include<queue>
#include<vector>
#include<map>
#include<stdlib.h>
#include<time.h>
#include<algorithm>
#define LL __int64
#define FIN freopen("in.txt","r",stdin)
using namespace std;
const int MAXN=100000+5;
const int MAX=1<<21;
const int INF=0x3f3f3f3f;
int a[MAX+5],num[MAXN];
int kase,n;
void init()
{
    for(int i=0;i<=MAX;i++)
    {
        int cnt=0;
        for(int j=0;j<21;j++)
            if(i & (1<<j))
                cnt++;
        a[i]=cnt;
    }
}
int main()
{
    init();
    scanf("%d",&kase);
    while(kase--)
    {
        scanf("%d",&n);
        for(int i=0;i<n;i++)
            scanf("%x",&num[i]);
        int ans=INF;
        srand( (unsigned)time( NULL ) );
        for(int i=0;i<900000;i++)
        {
            int x=rand()%n;
            int y=rand()%n;
            if(x==y) continue;
            ans=min(ans,a[num[x]^num[y]]);
        }
        printf("%d\n",ans);
    }
    return 0;
}