#pragma GCC optimize("-Ofast","-funroll-all-loops")
#pragma GCC optimize(2)
#pragma GCC optimize(3,"Ofast","inline")
#include<bits/stdc++.h>
using namespace std;

typedef long long ll;
int _;
int n;
int a[30010];

void solve(){
    cin >> _;
    while(_--){
        cin >> n;
        int cnt0 = 0, cnt1 = 0, cnt2 = 0;
        for(int i = 1; i <= n; i++){
            cin >> a[i];
            if(a[i] % 3 == 0){
                cnt0++;
            }
            else if(a[i] % 3 == 1){
                cnt1++;
            }
            else{
                cnt2++;
            }
        }
        int need = n/3;
        if(cnt0 == need && cnt1 == need && cnt2 == need){
            cout << "0" << "\n";
        }
        else if(cnt0 > need && cnt1 > need && cnt2 < need){
            cout << (cnt0-need)*2 + (cnt1-need) << "\n";
        }
        else if(cnt0 < need && cnt1 > need && cnt2 > need){
            cout << (cnt1-need)*2+(cnt2-need) << "\n";
        }
        else if(cnt0 > need && cnt1 < need && cnt2 > need){
            cout << (cnt0-need) + (cnt2-need)*2 << "\n";
        }
        else if(cnt0 > need && cnt1 < need && cnt2 < need){
            cout << (need-cnt1) + (need-cnt2)*2 << "\n";
        }
        else if(cnt0 < need && cnt1 > need && cnt2 < need){
            cout << (need-cnt2) + 2*(need-cnt0) << "\n";
        }
        else if(cnt0 < need && cnt1 < need && cnt2 > need){
            cout << (need-cnt0) + 2*(need-cnt1) << "\n";
        }
        else if(cnt0 == need){
            if(cnt1 > need && cnt2 < need){
                cout << (cnt1-need) << "\n";
            }
            else{
                cout << 2*(cnt2-need) <<"\n";
            }
        }
        else if(cnt1 == need){
            if(cnt0 > need && cnt2 < need){
                cout << 2*(cnt0-need) << "\n";
            }
            else{
                cout << (cnt2-need) << "\n";
            }
        }
        else if(cnt2 == need){
            if(cnt0 > need && cnt1 < need){
                cout << (cnt0 - need) << "\n";
            }
            else{
                cout << 2*(cnt1 - need) << "\n";
            }
        }
    }
    return ;
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    
    solve();
    return 0;
}
