ONP - Transform the Expression in Pyhton

https://www.spoj.com/problems/ONP/

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+^*