Description

Infix notation: X + Y

• Operators are written in-between their operands. This is the usual way we write expressions. An expression such as A * ( B + C ) / D is usually taken to mean something like: "First add B and C together, then multiply the result by A, then divide by D to give the final answer."

 

Prefix notation (also known as "Polish notation"): + X Y

• Operators are written before their operands. The expressions given above are equivalent to / * A + B C D

 

Now, please write a program to convert the given expressions from prefix to infix.

Input

The first line contains a positive integer N, indicating the number of testcases in this input.

In the following N lines, each line contains a prefix expression.

In each prefix expression, there is a space between numbers and operators, and operators and operators.

Output

Output the infix expression and its answer of each given prefix expression.

Note that

• There is a space between numbers and operators, and operators and operators.
• If the answer is integer, there is no need to print decimal point. Otherwise, you should print only one digit after the decimal point.
• You have to print a '\n' at the end of each ouput.
• Add a pair of parentheses to wrap around each operator and its operands.

Sample Input  Download

Sample Output  Download

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