public static void main ( String [ ] args ) {
  Scanner sc = new Scanner ( System . in ) ;
  int t = sc . nextInt ( ) ;
  while ( t -- > 0 ) {
    int n = sc . nextInt ( ) ;
    int [ ] a = new int [ n ] ;
    for ( int i = 0 ;
    i < n ;
    i ++ ) a [ i ] = sc . nextInt ( ) ;
    int res = 0 ;
    int [ ] cnt = new int [ 3 ] ;
    for ( int i = 0 ;
    i < n ;
    i ++ ) cnt [ a [ i ] % 3 ] ++ ;
    while ( Math . min ( cnt [ 0 ] , Math . min ( cnt [ 1 ] , cnt [ 2 ] ) ) != n / 3 ) {
      for ( int i = 0 ;
      i < 3 ;
      i ++ ) if ( cnt [ i ] > n / 3 ) {
        res ++ ;
        cnt [ i ] -- ;
        cnt [ ( i + 1 ) % 3 ] ++ ;
      }
    }
    System . out . println ( res ) ;
  }
}

public static void main ( String [ ] args ) { Scanner sc = new Scanner ( System . in ) ; int t = sc . nextInt ( ) ; while ( t -- > 0 ) { int n = sc . nextInt ( ) ; int [ ] a = new int [ n ] ; for ( int i = 0 ; i < n ; i ++ ) a [ i ] = sc . nextInt ( ) ; int res = 0 ; int [ ] cnt = new int [ 3 ] ; for ( int i = 0 ; i < n ; i ++ ) cnt [ a [ i ] % 3 ] ++ ; while ( Math . min ( cnt [ 0 ] , Math . min ( cnt [ 1 ] , cnt [ 2 ] ) ) != n / 3 ) { for ( int i = 0 ; i < 3 ; i ++ ) if ( cnt [ i ] > n / 3 ) { res ++ ; cnt [ i ] -- ; cnt [ ( i + 1 ) % 3 ] ++ ; } } System . out . println ( res ) ; } }
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