Validate Mathematical Expression Parentheses

In this problem, you are given a mathematical expression as a string. The expression may contain digits (0-9), basic arithmetic operators (+, -, *, /), whitespace characters, and the symbols ( ), [ ], and { }. Your task is to check whether the expression has all its parentheses, brackets, and braces properly matched and nested.

An expression is considered valid if:

• Every opening symbol ((, [, {) is closed by its corresponding closing symbol (), ], }) in the correct order.
• No unmatched symbols remain.

Note that the expression does not need to be mathematically evaluated; you only need to verify the proper pairing of the symbols.

Example:

3 + (2 - (4 / 2) * [2 + {3 * 4}]) is valid, while 3 + (4 - 5] is not.

inputFormat

The input consists of a single line representing the mathematical expression which may include digits, operators, whitespace, and the symbols ( ), [ ], and { }.

For example:

3 + (2 - (4 / 2) * [2 + {3 * 4}])

outputFormat

Output a single line: True if the expression is valid (i.e. all brackets are correctly matched and nested), or False otherwise.

## sample

3 + (2 - (4 / 2) * [2 + {3 * 4}])

True