curr

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>

using namespace std;
using namespace __gnu_pbds;

typedef long long ll;
typedef unsigned long long ull;
typedef tree<int,null_type,less<>,rb_tree_tag,tree_order_statistics_node_update> indexed_set;

#define all(v) v.begin(),v.end()
#define rall(v) v.rbegin(),v.rend()
#define MOD 1000000007
#define PI 3.14159265
//#define ceil(a, b) ((a / b) + (a % b ? 1 : 0))
#define imin INT_MIN
#define imax INT_MAX
#define nl '\n'
#define modulo(a, b, m) ((a % m) * (b % m)) % m

void Start_Crushing() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
#ifndef ONLINE_JUDGE
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
#endif
}
//vector<int> dx = {0, 0, 1, -1, 1, 1, -1, -1}, dy = {1, -1, 0, 0, 1, -1, 1, -1};
//int dx[] = {0, 0, 1, -1}, dy[] = {1, -1, 0, 0};

void solve(){
    int n; cin >> n;
    map<int, int> rem;
    for(int i = 0; i < n; i++){
        int x; cin >> x;
        rem[x % 3]++;
    }
    ll sum = 0;

    pair<int, int> maxi = {imin, imin};
    for(auto& [x, y] : rem){
        if(y > maxi.second) maxi = {x, y};
    }
//   while(min + 1 < max)
//  5 4

    int diff = rem[maxi.first] - rem[(maxi.first + 1) % 3];
    sum += diff;
    rem[maxi.first] -= diff, rem[(maxi.first + 1) % 3] -= diff;


    cout << sum;
}

int main(){
    //freopen("equal.in", "r", stdin);
    Start_Crushing();
    int t = 1;
    /*is Single Test case?*/ cin >> t;
    while (t--) {
        solve();
        if(!t) break;
        cout << "\n";
    }

    return 0;
}