#include<iostream>
#include<algorithm>
#include<string>
#include<sstream>
#include<stack>
#include<vector>
#include<set>
#include<map>
#include<utility>
#include<queue>
#include<cstring>
#include<deque>
#include<tuple>
#include<list>
#include<cmath>
#include<cstdlib>
#include<iomanip>
#include<bitset>
#include<random>
#include<limits>
#include<chrono>
using namespace std;
using namespace std::chrono;
typedef long long ll;
string IntToString(ll a) 
{ 
    char x[100]; 
    sprintf(x, "%lld", a); 
    string s = x; 
    return s; 
} 

ll StringToInt(string a) 
{ 
    char x[100]; 
    ll res; 
    strcpy(x, a.c_str()); 
    sscanf(x, "%lld", &res); 
    return res; 
}
vector<string> split(string s,char b)
{
    vector<string>ans;
    string temp = "";
    for (int i=0;i<s.size();i++)
    {
        if (s[i]==b)
        {
            ans.push_back(temp);
            temp = "";
        }
        else
            temp+=s[i];
    }
    return ans;
}

/*-------------------------------------------------CODE STARTS HERE------------------------------------------------*/

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    //auto start = high_resolution_clock::now(); 

    //write your code here
    int t;
    cin>>t;
    while (t--)
    {
        int n;
        cin>>n;
        int arr[n];
        int c0=0,c1=0,c2=0;
        for (int i=0;i<n;i++)
        {
            cin>>arr[i];
            if (arr[i]%3==0)
            c0++;
            else if (arr[i]%3==1)
            c1++;
            else if (arr[i]%3==2)
            c2++;
        }

        long long val = n/3;
        long long ans=0;
        if (c0>val)
        {
            c1 += (c0-val);
            ans += (c0-val);
            c0 = val;
        }
        if (c1>val)
        {
            c2 += (c1-val);
            ans += (c1-val);
            c1 = val;
        }
        if (c2>val)
        {
            c0 += (c2-val);
            ans += (c2-val);
            c2 = val;
        }
        if (c0>val)
        {
            c1 += (c0-val);
            ans += (c0-val);
            c0 = val;
        }
        if (c1>val)
        {
            c2 += (c1-val);
            ans += (c1-val);
            c1 = val;
        }
        if (c2>val)
        {
            c0 += (c2-val);
            ans += (c2-val);
            c2 = val;
        }
        cout<<ans<<'\n';

    }
    
    /* auto stop = high_resolution_clock::now(); 
        auto duration = duration_cast<microseconds>(stop - start); 

    cout << "Time taken by function: "
        << duration.count() << " microseconds" << endl; 
        */

    return 0;
}