Valid Arithmetic Expression Checker

You are given an arithmetic expression as a string. Your task is to determine whether the expression is valid based on the following rules:

• The expression may only contain non‐negative integer digits (0-9), the operators +, -, *, /, and parentheses ( and ).
• The expression should not contain any spaces or invalid characters.
• Operators cannot appear consecutively, and the expression cannot start or end with an operator.
• Parentheses must be balanced and non-empty.
• Division by zero is not allowed (e.g. evaluating an expression that causes a division by zero makes it invalid).

For example, the expression 3+(4-5)*2 is valid, while 5++6 or 10/(5-5) are invalid.

Your program should read the expression from standard input and print True if it is valid, or False otherwise.

inputFormat

The input consists of a single line containing the arithmetic expression to be validated. The expression does not contain any spaces.

outputFormat

Output a single line: True if the expression is valid, and False otherwise.

## sample

3+(4-5)*2

True

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