Balanced Brackets

Given a string containing only the characters (, ), {, }, [, and ], determine if the input string is valid using the following rules:

• Every opening bracket must have a corresponding closing bracket of the same type.
• Brackets must be closed in the correct order.

For example, the string () is valid, while the string (] is not. The solution should implement a function using a stack-based approach to verify balanced brackets. In cases where the input string is empty, consider it as balanced.

The formal conditions of validity can be expressed in LaTeX:

$$ \text{For a string } s \text{ to be valid, if } s = x\,y, \text{ then } x \text{ and } y \text{ must both be valid, and if } s = \{a\}, \text{ then } a \text{ must be valid.} $$

inputFormat

The input is provided via standard input (stdin) and consists of a single line containing a non-empty string of brackets. The string includes only the characters (, ), {, }, [, and ].

outputFormat

The output should be printed to standard output (stdout) as a single line: True if the string is balanced, and False otherwise.

## sample

()

True

</p>