A bracket is considered to be any one of the following characters: (, ), {, }, [, or ].

Two brackets are considered to be a matched pair if the an opening bracket (i.e., (, [, or {) occurs to the left of a closing bracket (i.e., ), ], or }) of the exact same type. There are three types of matched pairs of brackets: [], {},and ().

A matching pair of brackets is not balanced if the set of brackets it encloses are not matched. For example, {[(])} is not balanced because the contents in between { and } are not balanced. The pair of square brackets encloses a single, unbalanced opening bracket, (, and the pair of parentheses encloses a single, unbalanced closing square bracket, ].

By this logic, we say a sequence of brackets is balanced if the following conditions are met:

It contains no unmatched brackets.

The subset of brackets enclosed within the confines of a matched pair of brackets is also a matched pair of brackets.

Given string of brackets, determine whether the sequence of brackets is balanced. If a string is balanced, print YES. Otherwise, print NO.

Input Format

A single string s represents a sequence of brackets.

Output Format

Print YES or NO.

Sample Input

{[()]}

Sample Output

YES