As the problem title says, you are given a string **S** in infix form which you need to convert to postfix form. The expression contains operands from the set of uppercase English alphabets, operators from the set **{+,-*,/}**. Also there may be rounded parentheses '()' in the expression. There will be no other character in the string. The operators have the following properties:

- Expressions within brackets are always evaluated first.
- Multiplication(*) and Division(/) have the same precedence. Similarly, Addition(+) and Subtraction(-) have same precedence. But, + and / have higher precedence than + and -.
- All operators have left to right associativity.

The first line contains the number of test cases T (≤ 50). Each of the next T lines contains a string S (|S| ≤ 100), which is in infix form and contains characters as described above. The given expression will always be a valid infix expression.

For each test case output one line which is the postfix form for the given expression. Note that parentheses are not printed in the postfix form.

2 A*(B+C) (X*Y+Z)

ABC+* XY*Z+