#include <bits/stdc++.h>
using namespace std;

#define int long long
#define ld long double

#define rep(i,a,b) for(int i=a;i<b;i++)
#define repb(i,a,b) for(int i=a;i>b;i--)

#define pb push_back
#define mp make_pair
#define all(A) A.begin(),A.end()
#define allr(A) A.rbegin(),A.rend()
#define precise(i) fixed << setprecision(i)
#define fi first
#define se second

#define err() cout<<"\n==================================\n";
#define errA(A) for(auto i:A) cout<<i<<" "; cout<<"\n";
#define err1(a) cout<<#a<<" "<<a<<"\n";
#define err2(a,b) cout<<#a<<" "<<a<<" "<<#b<<" "<<b<<"\n";
#define err3(a,b,c) cout<<#a<<" "<<a<<" "<<#b<<" "<<b<<" "<<#c<<" "<<c<<"\n";
#define err4(a,b,c,d) cout<<#a<<" "<<a<<" "<<#b<<" "<<b<<" "<<#c<<" "<<c<<" "<<#d<<" "<<d<<"\n";

const int logN = 20;
const int M = 1000000007;
const int INF = 1e12;
#define PI 3.14159265;
const int N = 200005;

#define Pii pair<int,int>
#define Vi vector<int>
#define Vpii vector<Pii>

void solve()
{
    int n, ans=0;
    cin>>n;
    Vi a(n);
    rep(c,0,n)
    {
    	cin>>a[c];
    }
    int m0=0, m1=0, m2=0;
    rep(c,0,n)
    {
    	if(a[c]%3 == 0)
    	{
    		m0++;
    	}
    	else if(a[c]%3 == 1)
    	{
    		m1++;
    	}
    	else
    	{
    		m2++;
    	}
    }
    int final= n/3;
    while(m0 > final)
    {
    	m0--;
    	m1++;
    	ans++;
    }
    while(m1 > final)
    {
    	m1--;
    	m2++;
    	ans++;
    }
    while(m2 > final)
    {
    	m2--;
    	m0++;
    	ans++;
    }
    while(m0 > final)
    {
    	m0--;
    	m1++;
    	ans++;
    }
    while(m1 > final)
    {
    	m1--;
    	m2++;
    	ans++;
    }
    cout<<ans<<"\n";
}

int32_t main()
{
    ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
    int t=1;
    cin>>t;
    while(t--)
    {
        solve();
    }
    return 0;
}