Validate Mathematical Equations

You are given a set of mathematical equations represented as strings. Your task is to design a program that checks whether each equation is valid according to the following criteria:

• The equation must only contain digits, the decimal point, arithmetic operators (+, -, *, /), parentheses ( ), and spaces.
• Parentheses must be properly opened and closed, and nested correctly. In LaTeX, this condition is represented as: \(\text{for every opening } ( \text{ there is a matching } )\).
• The equation should not start or end with an operator. That is, the first and last non-space characters should not be any of \(+, -, *, /\).
• No two operators should appear consecutively unless they are separated by a valid parenthesized expression. For example, 3++2-1 is invalid, and so is (1+2)*-3.
• Both integers and floating point numbers are allowed as operands.

Your program will read an integer n from standard input, followed by n lines where each line is a mathematical equation. For each equation, output True if it meets all the criteria above, otherwise output False. Each result should be printed on a new line.

inputFormat

The input is read from stdin and has the following format:

 n
 equation_1
 equation_2
 ...
 equation_n

Here, n is an integer that denotes the number of equations to validate. Each subsequent line contains one equation as a string.

outputFormat

For each equation provided in the input, output either True or False (each on a new line) to stdout indicating whether the equation is valid according to the criteria described in the problem statement.

## sample

4
3+2-1
(1+2)*3
3*(2+1)
2.5+3.1

True
True
True
True

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