BalancedRemainderCF

// AUTHOR: fireLUFFYY, NITR
// Bhagwan, please AC karwa dena

#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,fma")
#pragma GCC optimize("unroll-loops")
#pragma comment(linker, "/stack:200000000")

#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
#define int long long
#define ull unsigned long long
#define vi vector<int>
#define vvl vector<vector<int>>
#define deql deque<int>
#define prquel priority_queue<int>
#define loop(i,n) for(int i=0;i<n;i++)
#define loopn(i,a,b) for(int i=a;i<=b;i++)
#define rloop(i,n) for(int i=n;i>0;i--)
#define sortv(a) sort(a.begin(),a.end())
#define sortvr(a) sort(a.rbegin(),a.rend())
#define verase(a) a.erase(unique(a.begin(),a.end()),a.end())
#define all(a) a.begin(),a.end()
#define getv(v,n) for(int i=0;i<n;i++){int x; cin>>x; v.push_back(x);};
#define dbg(x) cerr<<#x<<" = "; _print(x);cerr<<"\n";
#define mp make_pair
#define pb push_back
#define pf push_front
#define fi first
#define se second
#define endl "\n"
#define inf 2e18
using namespace std;
using namespace __gnu_pbds;

int MOD=1000000007;
int mod=998244353;
const int N=200050;
const int nn=1000050;
int fact[N]; // array to store values of factorial
bool prime[nn]; //array to store precalculated primes till 10^6
void _print(int a){cerr<<a;}  void _print(char a){cerr<<a;}  void _print(bool a){cerr<<a;}  void _print(string a){cerr<<a;}
template<class T> void _print(vector<T> v1){ cerr<<"[ "; for(T i:v1){_print(i);cerr<<" ";}cerr<<"]";}
template<class T> void _print(set<T> s1){ cerr<<"[ "; for(T i:s1){_print(i);cerr<<" ";}cerr<<"]";}
typedef tree<int,null_type,less<int>,rb_tree_tag,tree_order_statistics_node_update> indexed_set;
template<class T> T gcd(T a,T b){if(!a||!b)return a|b; unsigned shift=__builtin_ctz(a|b); a>>=__builtin_ctz(a); do{b>>=__builtin_ctz(b); if(a>b)swap(a,b);b-=a;}while(b); return a<<shift;}
template<class T> T lcm(T a,T b){ unsigned val=max(a,b)/gcd(a,b);val*=min(a,b);return val;}
bool pow2(int x){if(x&&(!(x&(x-1)))) return true; else return false;}
int multiply(int x, int y){return (x * 1ll * y) % MOD;}
int power(int x, int y){int z = 1;while(y){if(y & 1) z = multiply(z, x);x = multiply(x, x);y >>= 1;}return z;}
int modInverse(int x){return power(x, MOD - 2);}
int divide(int x, int y){return multiply(x, modInverse(y));}
void cal_factorial(){fact[0] = 1;for(int i = 1; i < N; i++)fact[i] = multiply(fact[i - 1], i);}// function to calculate factorial upto N
void cal_primes(){memset(prime,true,sizeof(prime)); loopn(i,2,sqrt(nn)){ if(prime[i]==true){ for(int j=i*i;j<=nn;j+=i){prime[j]=false;}}}}
int nCr(int n, int k){return divide(fact[n], multiply(fact[k], fact[n - k]));}
vector<int>Intersection(vi &v1,vi &v2){vi v3;sort(all(v1));sort(all(v2));set_intersection(all(v1),all(v2),back_inserter(v3));return v3;}
vector<int>Union(vi &v1,vi&v2){vi v3;sort(all(v1));sort(all(v2));set_union(all(v1),all(v2),back_inserter(v3));return v3;}
void FASTIO(){ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);}


void solve(int t)
{
    int testcases=t;
    while(t--)
    {
        //cout<<"#"<<(testcases-t)<<" Test-Case: "<<endl;
        //cout<<"Case #"<<(testcases-t)<<": ";
        int n,x,ans=0,dif;
        cin>>n;
        bool flag=true;
        int a[3]={0,0,0};
        loop(i,n)
        {
            cin>>x;
            a[x%3]++;
        }
        int avg=(n/3);
        while(flag)
        {
            flag=false;
            loop(i,3)
            {
                if(a[i]>avg)
                {
                    flag=true;
                    dif=(a[i]-avg);
                    a[(i+1)%3]+=dif;
                    a[i]-=dif;
                    ans+=dif;
                }
            }
        }
        cout<<ans<<endl;
    }
}

main()
{
    auto start=chrono::system_clock::now();
    {
        #ifndef ONLINE_JUDGE
            freopen("input.txt","r",stdin);
            freopen("output.txt","w",stdout);
            freopen("error.txt","w",stderr);
        #endif
        FASTIO();
        int t=1;
        cin>>t;
        solve(t);
    }
    auto end=chrono::system_clock::now();
    chrono::duration<double> elapsed=end-start;
//  cout<<" Time taken: "<<elapsed.count()<<" sec";
    return 0;
}