#include <bits/stdc++.h>   using namespace std;   typedef long long ll;      inline int read(){       int x=0,f=1;       char ch=getchar();       while(ch< 0 ||ch> 9 ){           if(ch== - )               f=-1;           ch=getchar();       }       while(ch>= 0 &&ch<= 9 ){           x=(x<<1)+(x<<3)+(ch^48);           ch=getchar();       }       return x*f;   }   const int maxn = 3e4 + 9;    int t;   int a[3];   int solve(){    int l = a[0], m = a[1], r = a[2];    int avg = (l + m + r) / 3;    //printf( avg: %d n , avg);    int ans = 0;    if (l < avg){     if (r > avg){      if (m > avg){       ans += (m - avg) * 2 + r - avg;       return ans;      }      else if (m < avg){       ans += avg - l + (avg - m) * 2;       return ans;      }      else{       ans += avg - l;       return ans;      }     }     else if (r < avg){      ans += (avg - l) * 2 + avg - r;      return ans;     }     else{      ans += (avg - l) * 2;      return ans;     }    }    else if (l == avg){     if (m == avg){      return ans;     }     else if (m < avg){      ans += (avg - m) * 2;      return ans;     }     else{      ans += m - avg;      return ans;     }    }    else{     if (m < avg){      if (r > avg){       ans += (r - avg) * 2 + l - avg;       return ans;      }      else if (r < avg){       ans += (avg - r) * 2 + avg - m;       return ans;      }      else{       ans += avg - m;       return ans;      }     }     else if (m > avg){      ans += (l - avg) * 2 + m - avg;      return ans;     }     else{      ans = (l - avg) * 2;      return ans;     }    }    return ans;   }   int main(){       t = read();       while(t--){        int n = read();        int m;        a[0] = a[1] = a[2] = 0;        for (int i = 1; i <= n; i++){         m = read();         a[m % 3]++;     }     //sort(a, a + 3);     int ans = solve();     printf( %d n , ans);    }    return 0;   }   