# Convert to Postfix Notation

In Reverse Polish Notation (RPN), also known as postfix notation, each operator follows all of its operands. For example, instead of writing "3 + 4" for addition, one would write "3 4 +". When dealing with multiple operations, the operator is placed immediately after its second operand. Thus, what is normally written as "3 - 4 + 5" in conventional notation, would be expressed as "3 4 - 5 +" in RPN, where you first subtract 4 from 3, and then add 5 to the result.

Your task is to convert an algebraic expression that may contain brackets into its equivalent RPN form.

For the purposes of this challenge, assume that all test cases will use single letters for variables, square brackets [] will be avoided, and each expression will have a unique RPN form (complexities like a*b*c are not included).

## Input Format

- The first line specifies t, the number of test cases (less than 100).
- This is followed by t lines, each containing an algebraic expression that needs to be converted into RPN form, with each expression being less than 400 characters long.

## Output Format

Output the *converted expressions* in RPN form, with each expression on a new line.

## Constraints

## Example Input and Output

### Example #1:

Input:

`3 (a+(b*c)) ((a+b)*(z+x)) ((a+t)*((b+(a+c))^(c+d)))`

Output:

`abc*+ ab+zx+* at+bac++cd+^*`