Problem:
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.

Sample Input 1

3
0 ( 10
10 ) 5
10 ) 5

Output for the Sample Input 1

No
No
Yes

Sample Input 2

3
0 ) 10
10 ( 5
10 ( 5

Output for the Sample Input 2

No
No
Yes

Sample Input 3

3
0 ( 10
10 ) 20
0 ( 10

Output for the Sample Input 3

No
No
Yes

Solution in Scala (judge verdict: Accepted)

object Main extends App {

  import scala.io.StdIn._
  import scala.math._
  var left = 0L
  for (_ ← 0 until readLine.trim.toInt){
    val Array(_, direction, length) = readLine.trim.split(' ')
    direction match {
      case "(" ⇒ left += length.toInt
      case _ ⇒ left -= length.toInt
    }
    println(
      if (left == 0) "Yes"
      else "No"
    )
  }
  implicit class Extension[T](val value :T){
    def also(func: T ⇒ Unit): T = {
      func(value)
      value
    }
    def let[R](func: T ⇒ R): R = func(value)
  }
}