## Stack... ( Reverse Polish Notation or Infix To Post Fix)

A very common and classical problem which involves use of stack is to convert a given infix expression to a post fix expression or Reverse Polish Notation .

Transform the Expression:

Transform the Expression:

Transform the algebraic expression with brackets into RPN form (Reverse Polish Notation). Two-argument operators: +, -, *, /, ^ (priority from the lowest to the highest), brackets ( ). Operands: only letters: a,b,...,z. Assume that there is only one RPN form (no expressions like a*b*c).

### Input

t[the number of expressions <=100]expression[length <=400]

[other expressions]

Text grouped in [ ] does not appear in the input file.

### Output

Theexpressions in RPN form, one per line.

### Example

Input:

3

(a+(b*c))

((a+b)*(z+x))

((a+t)*((b+(a+c))^(c+d)))

Output:

abc*+

ab+zx+*

at+bac++cd+^*