Carpenters' Language

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.

Input

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.

Output

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

Examples

Input

3 0 ( 10 10 ) 5 10 ) 5

Output

No No Yes

Input

3 0 ) 10 10 ( 5 10 ( 5

Output

No No Yes

Input

3 0 ( 10 10 ) 20 0 ( 10

Output

No No Yes

inputFormat

outputFormat

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.

Input

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.

Output

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

Examples

Input

3 0 ( 10 10 ) 5 10 ) 5

Output

No No Yes

Input

3 0 ) 10 10 ( 5 10 ( 5

Output

No No Yes

Input

3 0 ( 10 10 ) 20 0 ( 10

Output

No No Yes

样例

3
0 ( 10
10 ) 20
0 ( 10

No
No
Yes

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