International Carpenters Professionals Company (ICPC) is a top construction company with a lot of expert carpenters. What makes ICPC a top company is their original language.

The syntax of the language is simply given in CFG as follows:

S -> SS | (S) | )S( | ε

In other words, a right parenthesis can be closed by a left parenthesis and a left parenthesis can be closed by a right parenthesis in this language.

Alex, a grad student mastering linguistics, decided to study ICPC's language. As a first step of the study, he needs to judge whether a text is well-formed in the language or not. Then, he asked you, a great programmer, to write a program for the judgement.

Alex's request is as follows: You have an empty string S in the beginning, and construct longer string by inserting a sequence of '(' or ')' into the string.
You will receive `q` queries, each of which consists of three elements `(p, c, n)`, where `p` is
the position to insert, `n` is the number of characters to insert and `c` is either '(' or ')', the character to insert.
For each query, your program should insert `c` repeated by `n` times into the `p`-th position of S from the beginning.
Also it should output, after performing each insert operation, "Yes" if S is in the language and "No" if S is not in the language.

Please help Alex to support his study, otherwise he will fail to graduate the college.

The first line contains one integer `q` (`1 \leq q \leq 10^5`) indicating the number of queries, follows
`q` lines of three elements, `p_i`, `c_i`, `n_i`, separated by a single space (`1 \leq i \leq q`, `c_i = '(' or ')'`,
`0 \leq p_i \leq ` length of S before `i`-th query, `1 \leq n \leq 2^{20}`).
It is guaranteed that all the queries in the input are valid.

For each query, output "Yes" if S is in the language and "No" if S is not in the language.

3 0 ( 10 10 ) 5 10 ) 5

No No Yes

3 0 ) 10 10 ( 5 10 ( 5

No No Yes

3 0 ( 10 10 ) 20 0 ( 10

No No Yes

Source: ACM-ICPC Japan Alumni Group Winter Contest 2012
, Tokyo, Japan, 2012-03-10

http://acm-icpc.aitea.net/

http://acm-icpc.aitea.net/