SPOJ ONP - Transform the Expression:Transform the algebraic expression with brackets into RPN form (Reverse Polish Notation). Two-argument operators:

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

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+^*

Solution (in Python) 

import  sys
def infixtopostfix(exp):
    output = ""    stack = []
    op_key = {'+':0,'-':0,'*':1,'/':2,'^':3}

    for i in range(0,len(exp)):
        if(exp[i] in op_key.keys()):
            while(len(stack)>0 and stack[len(stack)-1] != '(' and op_key[exp[i]]<=stack[len(stack)-1]):
                output += stack.pop()
            stack.append(exp[i])
        elif exp[i] == '(':
            stack.append('(')
        elif exp[i] == ')':
            while(len(stack)>0 and stack[len(stack)-1]!='('):
                output += stack.pop()
            if(len(stack)>0):
                stack.pop()
        else:
            output += exp[i]

    return output

T = int(input())
output_list = []
#print Twhile T>0:


    exp = sys.stdin.readline()
    exp = exp.strip("\n")
    output_list.append(infixtopostfix(exp))
    T-=1
for i in range(0,len(output_list)):
    print output_list[i]