Valid Parentheses Sequence Checker

You are given a string S consisting solely of the characters ('), ')', '{', '}', '[' and ']'. Your task is to determine whether the sequence of parentheses is valid.

A sequence is considered valid if:

• Every opening bracket has a corresponding closing bracket.
• Brackets are closed in the correct order.

An empty string is also considered valid.

This can be formally defined using the following recursive formulation:

$$\text{valid} = \epsilon \quad \text{or} \quad valid = (A) \quad \text{or} \quad valid = [A] \quad \text{or} \quad valid = \{A\} \quad \text{or} \quad valid = AB$$

where \(A\) and \(B\) are valid sequences.

inputFormat

The input is read from standard input (stdin). It consists of a single line containing the string S, which includes only the characters '(', ')', '{', '}', '[' and ']'.

outputFormat

Print a single line to standard output (stdout) containing "YES" if the sequence is valid, otherwise print "NO".## sample

()

YES