#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

const ll DIM = 1e6 + 7;
const ll INF = 1e16 + 7;
const ll MODULO = 1e9 + 7;

ll n,m,nt,k,q;

ll val,val1,last,res,c0,c1,c2;

int main()
{
    ios_base::sync_with_stdio();
    cin.tie();
    cout.tie();

    cin>>nt;
    for(int t=1; t<=nt; t++)
    {

        cin>>n;

        res=0;
        c0=0;
        c1=0;
        c2=0;

        for(int i=1; i<=n; i++)
        {
            cin>>val;

            if(val%3==0)c0++;
            else if(val%3==1)c1++;
            else c2++;
        }

        for(int i=1; i<=2; i++)
        {

            if(c0>n/3)
            {
                val=c0-n/3;
                res+=val;
                c1+=val;
                c0-=val;
            }

            if(c1>n/3)
            {
                val=c1-n/3;
                res+=val;
                c2+=val;
                c1-=val;
            }

            if(c2>n/3)
            {
                val=c2-n/3;
                res+=val;
                c0+=val;
                c2-=val;
            }
        }

        cout<<res<<endl;
    }

    return 0;
}
