public static void main ( String [ ] args ) {
  Scanner sc = new Scanner ( System . in ) ;
  int t = sc . nextInt ( ) ;
  while ( t -- > 0 ) {
    int n = sc . nextInt ( ) ;
    int [ ] arr = new int [ n ] ;
    int [ ] brr = new int [ 1001 ] ;
    Vector < Integer > v = new Vector < > ( ) ;
    for ( int i = 0 ;
    i < n ;
    i ++ ) {
      arr [ i ] = sc . nextInt ( ) ;
      v . add ( arr [ i ] ) ;
    }
    for ( int i = 0 ;
    i < n ;
    i ++ ) brr [ arr [ i ] ] = - 1 ;
    int c = 1 , done = 0 ;
    for ( int i = 2 ;
    i <= 1000 ;
    i ++ ) {
      for ( int j = i * i ;
      j <= 1000 ;
      j += i ) {
        if ( brr [ j ] == - 1 ) {
          brr [ j ] = c ;
          done = 1 ;
        }
      }
      if ( done == 1 ) {
        done = 0 ;
        c ++ ;
      }
    }
    done = 0 ;
    for ( int i = 0 ;
    i < n ;
    i ++ ) {
      if ( brr [ arr [ i ] ] == - 1 ) {
        brr [ i ] = c ;
        done = 1 ;
      }
      if ( done == 1 ) {
        done = 0 ;
        c ++ ;
      }
    }
    HashSet < Integer > set = new HashSet < > ( ) ;
    for ( int i = 0 ;
    i < n ;
    i ++ ) {
      if ( brr [ arr [ i ] ] != - 1 ) set . add ( brr [ arr [ i ] ] ) ;
    }
    System . out . println ( set . size ( ) ) ;
    for ( int i = 0 ;
    i < n ;
    i ++ ) {
      if ( brr [ arr [ i ] ] != - 1 ) System . out . print ( brr [ arr [ i ] ] + " " ) ;
    }
    System . out . println ( ) ;
  }
}

public static void main ( String [ ] args ) { Scanner sc = new Scanner ( System . in ) ; int t = sc . nextInt ( ) ; while ( t -- > 0 ) { int n = sc . nextInt ( ) ; int [ ] arr = new int [ n ] ; int [ ] brr = new int [ 1001 ] ; Vector < Integer > v = new Vector < > ( ) ; for ( int i = 0 ; i < n ; i ++ ) { arr [ i ] = sc . nextInt ( ) ; v . add ( arr [ i ] ) ; } for ( int i = 0 ; i < n ; i ++ ) brr [ arr [ i ] ] = - 1 ; int c = 1 , done = 0 ; for ( int i = 2 ; i <= 1000 ; i ++ ) { for ( int j = i * i ; j <= 1000 ; j += i ) { if ( brr [ j ] == - 1 ) { brr [ j ] = c ; done = 1 ; } } if ( done == 1 ) { done = 0 ; c ++ ; } } done = 0 ; for ( int i = 0 ; i < n ; i ++ ) { if ( brr [ arr [ i ] ] == - 1 ) { brr [ i ] = c ; done = 1 ; } if ( done == 1 ) { done = 0 ; c ++ ; } } HashSet < Integer > set = new HashSet < > ( ) ; for ( int i = 0 ; i < n ; i ++ ) { if ( brr [ arr [ i ] ] != - 1 ) set . add ( brr [ arr [ i ] ] ) ; } System . out . println ( set . size ( ) ) ; for ( int i = 0 ; i < n ; i ++ ) { if ( brr [ arr [ i ] ] != - 1 ) System . out . print ( brr [ arr [ i ] ] + " ▁ " ) ; } System . out . println ( ) ; } }
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