public static void main ( String [ ] args ) {
  Scanner sc = new Scanner ( System . in ) ;
  int cases = sc . nextInt ( ) ;
  while ( cases > 0 ) {
    int n = sc . nextInt ( ) ;
    int [ ] arr = new int [ 3 ] ;
    for ( int i = 0 ;
    i < n ;
    i ++ ) {
      arr [ sc . nextInt ( ) % 3 ] ++ ;
    }
    int count = 0 ;
    while ( arr [ 0 ] != arr [ 1 ] || arr [ 0 ] != arr [ 2 ] ) {
      for ( int i = 0 ;
      i < 3 ;
      i ++ ) {
        if ( arr [ i ] > n / 3 ) {
          arr [ i ] -- ;
          arr [ ( i + 1 ) % 3 ] ++ ;
          count ++ ;
        }
      }
    }
    System . out . println ( count ) ;
    cases -- ;
  }
}

public static void main ( String [ ] args ) { Scanner sc = new Scanner ( System . in ) ; int cases = sc . nextInt ( ) ; while ( cases > 0 ) { int n = sc . nextInt ( ) ; int [ ] arr = new int [ 3 ] ; for ( int i = 0 ; i < n ; i ++ ) { arr [ sc . nextInt ( ) % 3 ] ++ ; } int count = 0 ; while ( arr [ 0 ] != arr [ 1 ] || arr [ 0 ] != arr [ 2 ] ) { for ( int i = 0 ; i < 3 ; i ++ ) { if ( arr [ i ] > n / 3 ) { arr [ i ] -- ; arr [ ( i + 1 ) % 3 ] ++ ; count ++ ; } } } System . out . println ( count ) ; cases -- ; } }
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