public static void main ( String [ ] args ) {
  Scanner input = new Scanner ( System . in ) ;
  int t = input . nextInt ( ) ;
  for ( int j = 0 ;
  j < t ;
  j ++ ) {
    int n = input . nextInt ( ) ;
    int [ ] a = new int [ 3 ] ;
    for ( int i = 0 ;
    i < n ;
    i ++ ) {
      int c = input . nextInt ( ) ;
      a [ c % 3 ] ++ ;
    }
    int count = 0 ;
    n /= 3 ;
    for ( int i = 0 ;
    i < 5 ;
    i ++ ) {
      if ( a [ i % 3 ] > n ) {
        a [ ( i + 1 ) % 3 ] += a [ i % 3 ] - n ;
        count += a [ i % 3 ] - n ;
        a [ i % 3 ] = n ;
      }
    }
    System . out . println ( count ) ;
  }
}

public static void main ( String [ ] args ) { Scanner input = new Scanner ( System . in ) ; int t = input . nextInt ( ) ; for ( int j = 0 ; j < t ; j ++ ) { int n = input . nextInt ( ) ; int [ ] a = new int [ 3 ] ; for ( int i = 0 ; i < n ; i ++ ) { int c = input . nextInt ( ) ; a [ c % 3 ] ++ ; } int count = 0 ; n /= 3 ; for ( int i = 0 ; i < 5 ; i ++ ) { if ( a [ i % 3 ] > n ) { a [ ( i + 1 ) % 3 ] += a [ i % 3 ] - n ; count += a [ i % 3 ] - n ; a [ i % 3 ] = n ; } } System . out . println ( count ) ; } }
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