A feature flag stream is a string of the characters (, ), and *. Each * is a wildcard that may be treated as a single (, a single ), or an empty string. Decide whether there is some assignment of the wildcards that makes the whole string a valid balanced parenthesis string.

A string is a valid balanced parenthesis string when it is empty, or it is two valid strings concatenated, or it is ( followed by a valid string followed by ). Equivalently: reading left to right the number of ) never exceeds the number of (, and the totals are equal at the end.

Input format

A single line: the stream (it may be empty). It contains only the characters (, ), and *.

Output format

Print YES if some wildcard assignment yields a valid balanced string, otherwise NO.

Constraints

• 0 <= length of the stream <= 100
• The stream contains only (, ), and *.

(*)

YES

)(

NO