AT_abc428_c [ABC428C] Brackets Stack Query

A string $ T $ is called a good bracket sequence if and only if it satisfies the following condition: - $ T $ can be made into an empty string by repeating the following operation zero or more times: - Choose `()` contained in $ T $ as a (contiguous) substring and remove it. For example, `()`, `(()())`, and the empty string are good bracket sequences, but `)()(` and `)))` are not good bracket sequences. There is a string $ S $ . Initially, $ S $ is an empty string. Process $ Q $ queries in the order they are given. After each query, determine whether $ S $ is a good bracket sequence. There are two types of queries: - `1 c`: A character $ c $ is given. $ c $ is either `(` or `)`. Append $ c $ to the end of $ S $ . - `2`: Remove the last character of $ S $ . It is guaranteed that $ S $ is not an empty string at this time.

The input is given from Standard Input in the following format, where $ \mathrm{query}_i $ denotes the $ i $ -th query. > $ Q $ $ \mathrm{query}_1 $ $ \mathrm{query}_2 $ $ \vdots $ $ \mathrm{query}_Q $ Each query is given in one of the following two formats: > $ 1 $ $ c $ > $ 2 $

Output $ Q $ lines. The $ i $ -th line should contain `Yes` if the string $ S $ immediately after processing the $ i $ -th query is a good bracket sequence, and `No` otherwise.

### Sample Explanation 1 $ S $ immediately after processing the $ 1 $ st query is `(`, which is not a good bracket sequence. $ S $ immediately after processing the $ 2 $ nd query is an empty string, which is a good bracket sequence. $ S $ immediately after processing the $ 3 $ rd query is `(`, which is not a good bracket sequence. $ S $ immediately after processing the $ 4 $ th query is `()`, which is a good bracket sequence. $ S $ immediately after processing the $ 5 $ th query is `(`, which is not a good bracket sequence. $ S $ immediately after processing the $ 6 $ th query is `((`, which is not a good bracket sequence. $ S $ immediately after processing the $ 7 $ th query is `(()`, which is not a good bracket sequence. $ S $ immediately after processing the $ 8 $ th query is `(())`, which is a good bracket sequence. ### Constraints - $ 1 \leq Q \leq 8 \times 10^5 $ - $ c $ in queries of the first type is `(` or `)`. - It is guaranteed that $ S $ is not empty when a query of the second type is given. - $ Q $ is an integer.