
114  ZOJ 10th Anniversary Contest  E
In computer program, there is a kind of expression, called boolean expressions. In this kind of expressions, the variables have only two values, T (TRUE) or F (FALSE) while the result can only be T or F too. All the variables in this kind of expressions are connected with boolean operation (from the highest priority to the lowest priority): ! (not), & (and),  (or) and ^ (xor). The meaning of them are:
In the expressions, '(' and ')' are also used to get the higher priority inside the brackets. One boolean expression can have many equivalent forms. Two expressions are equivalent only if the results are the same no matter what value the variables are. Now your task is to write a program to check if two boolean expressions are equivalent. InputThe expressions are in groups in the input. Each group has two lines and one expression in each line. There are at most 200 characters in each line, at least 2 variables in each expression and no variable named as "TRUE" or "FALSE". There are at most 15 variables for each group of expressions, and each variable is a case sensitive string with at most 10 letters. Please note space can be used at proper place in the expression. An empty line means the end of input. OutputFor each group, you only need to output TRUE or FALSE in one line indicates if two expressions are equivalent. Sample InputA&(BC) (BC)&A A & B B  A Sample OutputTRUE FALSE Author: ZHOU, Ran 