AT_abc394_d [ABC394D] Colorful Bracket Sequence

You are given a string $ S $ consisting of six types of characters: `(`, `)`, `[`, `]`, ``. A string $ T $ is called a colorful bracket sequence if it satisfies the following condition: > It is possible to turn $ T $ into an empty string by repeating the following operation any number of times (possibly zero): > > - If there exists a contiguous substring of $ T $ that is one of `()`, `[]`, or ``, choose one such substring and delete it. > - If the deleted substring was at the beginning or end of $ T $ , the remainder becomes the new $ T $ . > - Otherwise, concatenate the part before the deleted substring and the part after the deleted substring, and that becomes the new $ T $ . Determine whether $ S $ is a colorful bracket sequence.

The input is given from Standard Input in the following format: > $ S $

If $ S $ is a colorful bracket sequence, print `Yes`; otherwise, print `No`.

### Sample Explanation 1 For $ S= $ `([])()`, it is possible to turn it into an empty string by repeating the operation as follows: - Delete the substring `[]` from the 2nd to the 3rd character in `([])()`, then concatenate the parts before and after it. The string becomes `()()`. - Delete the substring `()` from the 1st to the 2nd character in `()()`. The string becomes `()`. - Delete the substring `` from the 1st to the 2nd character in `()`. The string becomes `()`. - Delete the substring `()` from the 1st to the 2nd character in `()`. The string becomes empty. Thus, $ S= $ `([])()` is a colorful bracket sequence, so print `Yes`. ### Sample Explanation 2 Since $ S= $ `([` does not contain `()`, `[]`, or `` as a contiguous substring, we cannot perform the 1st operation, and in particular $ S $ is not a colorful bracket sequence. Therefore, print `No`. ### Sample Explanation 3 It is impossible to turn $ S $ into an empty string by repeating the operations. Therefore, $ S $ is not a colorful bracket sequence, so print `No`. ### Constraints - $ S $ is a string of length between $ 1 $ and $ 2\times 10^5 $ , inclusive. - $ S $ consists of `(`, `)`, `[`, `]`, ``.