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+^*

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