The exciting World Cup 2010's summer is coming! And Johnny's family shop is busy preparing a colorful lighting board for the summer.

The board has a rectangular shape of size M x N. There are certain positions on the board which Johnny wants to put in light bulbs.

Johnny wants to decorate the board by colorful light bulbs. To make the board look attractive, he wants the bulbs in the same column or row to have different colors! On the other hand, to preserve the harmony look, Johnny doesn't want the bulbs to have many different colors.

Given three numbers A, B and C all having N digits, little Johnny needs to write a program to permute the digits of the number C so that the new number is greater than both A and B.

This problem would be so easy if Johnny's teacher didn't require that Johnny's program must be correct in both the real world and the reversed world. What happens once the world is reversed? One thing Johnny knows for sure is that all the numbers are also reversed. The second thing, the "greater than" relation becomes the "smaller than" relation.