Problem $1$: Infix to Postfix Conversion

Infix : An expression is called the Infix expression if the operator appears in between the operands in the expression. Simply of the form $($operand$1$ operator operand$2).$

Example : $(A+B)**(C-D)$

Postfix : An expression is called the postfix expression if the operator appears in the expression after the operands. Simply of the form $($operand$1$ operand$2$ operator$).$

Example: $)$

Write a program that converts an infix $($fully parenthesized$)$ expression to a postfix expression. The program will have to handle only the binary operators $+,-,**\frac{,}{,{?}^{{?}^{?}}}.$ parenthesis, letters and numbers.

An example would be an expression like:

$(\frac{(A^{**}(B))+(2^{**}(C^3))}{2^{**}(A)}).$

The program must convert this expression $($infix$)$ to the postfix expression: $A{B}^{**}2C^{{?}^{{?}^{?}}**}+2\frac{A^{**}}{?}$ All expressions of the test cases are expressions with valid syntax.

You are given a InfixtoPostfix.java file fill in your code in that file.

Hint: Use one stack for operator $($you can use the Java built$-$in stack$).$

Input

Read input from a file $"$in$1.$txt$".$ Each input is a valid fully parenthesized expression in the infix notation.

Output

For each test case, print the expression converted to prefix expression.

$\backslash$table$[[$Input Sample,Output Sample$],[(A^{**}2),A{2}^{**}$