# 702 B
思路:先把c0 c1 c2记录下来然后依次循环移动,记录下移动次数就好
#include<stdio.h>
#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;
int ai[30010];
int main()
{
int t;
scanf("%d",&t);
while(t--)
{
int n;
int c0=0,c1=0,c2=0,c3=0;
scanf("%d", &n);
for(int i=1;i<=n;i++)
{
scanf("%d",&ai[i]);
if(ai[i]%3==0)c0++;
if(ai[i]%3==1)c1++;
if(ai[i]%3==2)c2++;
if(ai[i]==0)c3++;
}
int res=0;
if(c0==c1&&c1==c2)printf("0\n");
else
{
while(!(c0==c1&&c1==c2))
{
if(c0>c1)
{
res++;
c0--;
c1++;
}
if(c1>c2)
{
res++;
c1--;
c2++;
}
if(c2>c0)
{ res++;
c2--;
c0++;
}
}
printf("%d\n",res);
} }
return 0;
}