0.SVMC 2017 ONP - Transform the Expression


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Points: 1
Time limit: 1.0s
Memory limit: 10M

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Problem type

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 ab*c).

Input

t [the number of expressions <= 100] expression [length <= 400] [other expressions] Text grouped in [ ] does not appear in the input file.

Output

The expressions 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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