Equation 

Input and Output 

Write a program that changes an infix expression to a postfix expression according to the following specifications.

1.

The infix expression to be converted is in the input file in the format of one character per line, with a maximum of 50 lines in the file. For example, (3+2)*5 would be in the form:

(
3
+
2
)
*
5

2.

The input starts with an integer on a line by itself indicating the number of test cases. Several infix expressions follows, preceded by a blank line.

3.

The program will only be designed to handle the binary operators +, -, *, /.

4.

The operands will be one digit numerals.

5.

The operators * and / have the highest priority. The operators + and - have the lowest priority. Operators at the same precedence level associate from left to right. Parentheses act as grouping symbols that over-ride the operator priorities.

6.

The output file will have each postfix expression all on one line. Print a blank line between different expressions.

7.

Each testcase will be an expression with valid syntax.

Sample Input 

1

(
3
+
2
)
*
5

Sample Output 

32+5*