Basic Calculator Simulation

You are required to implement a basic calculator that evaluates a given mathematical expression represented as a string. The expression can include non-negative numbers and the operators +, -, *, and / along with parentheses. The evaluation must obey the standard order of operations, i.e. the precedence rules: addition and subtraction have lower precedence than multiplication and division. In mathematical notation, you should consider:

$$+,- \quad \text{(lowest precedence)}$$

$$*,/ \quad \text{(higher precedence)}$$

Your task is to parse and evaluate the expression without using built-in evaluation functions such as eval(). The calculator must also handle error cases: if division by zero occurs, the program should output:

ZeroDivisionError: Division by zero is not allowed.

If the expression is malformed or contains invalid characters (e.g. letters), the program should output:

ValueError: Invalid mathematical expression.

The input will be provided via standard input (stdin) as a single line containing the mathematical expression. The output should be printed on standard output (stdout) as a floating point number with one decimal place, or as an error message if an error occurs.

inputFormat

The input consists of a single line containing a string expression which represents a mathematical formula. The expression may include numbers, the operators +, -, *, /, and parentheses ( ).

outputFormat

If the expression is valid and no errors occur, output the evaluated result as a floating point number with exactly one decimal place. If a division by zero occurs, output the exact message:

ZeroDivisionError: Division by zero is not allowed.

For any other invalid expression, output:

ValueError: Invalid mathematical expression.

## sample

3+2

5.0