Integer Equation Checker

In this task you need to create a checker for integer equations with error correction.

The integer equation is given in the form:

<number1><operation><number2>=<number3>

wherein "<numberI>" denotes any positive integer less than or equal to $10^9$ without leading zeros, and "<operation>" is one of the signs '+', '-', '*' or '/' that represents one of the four basic math operations (note that unary plus and unary minus are not allowed). An expression that satisfies these properties is called well-formatted.

The checker shall read the equations and give the outcome in the next way:

• Correct --- a well-formatted mathematically correct equation is given.
• Format Error --- the given equation does not match the default format.
• Typo: <equation1> instead of <equation2> --- the given equation (<equation1>) is well-formatted but not mathematically correct and is is enough to replace up to two characters in it to obtain a mathematically correct and well-formatted equation (<equation2>).
• Math Error --- the given equation is well-formatted, mathematically incorrect, and it is impossible to correct two or less characters and obtain a well-formatted and mathematically correct equation.

Note that characters can be only replaced, they cannot be inserted or deleted.

The first line of the input contains a non-empty string of up to 30 characters that represents the equation to be checked. This word consists only of decimal digits ('0' - '9'), arithmetic operators ('+', '-', '*', and '/') and equality signs ('=').

Print the result of evaluation. Refer to the samples for clarity.