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John's college will hold a programming contest, and now it's calling for problems. John wants to contribute a problem to this contest. After finishing the problem, he found some trouble in verifying the programmer's output. For most programming problems, you can just compare the programmer's output against the correct answer, and if they are literally the same, the programmer's output is correct, otherwise it's wrong. But for this problem, there may be many correct answers and they can be different from each other literally. So John must write a program to verify programmers' output (We can call this program "Special Judge"). Soon, he found the Special Judge is too difficult for him, so he turns to you for help.