import java.util.Arrays;
import java.util.List;

public final class LargestNumberDivisibleByItsDigits {

   public static void main(String[] args) {
      // Base 10
      final int decimalDivisor = 9 * 8 * 7;
       int decimal = ( 9876432 / decimalDivisor ) * decimalDivisor;

       while ( ! isLynchBellDecimal(decimal) ) {
         decimal -= decimalDivisor;
       }
       System.out.println("The largest decimal Lynch-Bell number is " + decimal);

      // Base 16
      final long hexDivisor = 15L * 14 * 13 * 12 * 11;

       long hexadecimal = ( 0xfedcba987654321L / hexDivisor ) * hexDivisor;
       while ( ! isLynchBellHex(hexadecimal) ) {
         hexadecimal -= hexDivisor;
       }
       System.out.println("The largest hexadecimal Lynch-Bell number is " + Long.toHexString(hexadecimal));
   }

   private static boolean isLynchBellDecimal(int decimal) {
      String decimalString = Integer.toString(decimal);
        if ( decimalString.contains("0") || decimalString.contains("5") ) {
         return false;
        }

        List<Integer> distinctDigits =
         Arrays.stream(decimalString.split("")).map( s -> Integer.valueOf(s) ).distinct().toList();
        if ( distinctDigits.size() < decimalString.length() ) {
         return false;
        }

        return distinctDigits.stream().allMatch( i -> ( decimal % i ) == 0 );
   }

   private static boolean isLynchBellHex(long hexadecimal) {
      String hexString = Long.toHexString(hexadecimal);
      if ( hexString.contains("0") ) {
         return false;
      }

      List<Integer> distinctDigits =
         Arrays.stream(hexString.split("")).map( s -> Integer.valueOf(s, 16) ).distinct().toList();
      if ( distinctDigits.size() < hexString.length() ) {
         return false;
      }

      return distinctDigits.stream().allMatch( i -> ( hexadecimal % i ) == 0 );
   }

}