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 JAVA (judge verdict: Accepted)

import java.util.*;
import static java.lang.System.*;

public class Main {

	Scanner sc = new Scanner(in);
	
	void run() {
		int q = sc.nextInt();
		long num = 0L;
		int lr = 0;
		for (int i = 0; i < q; i++) {
			sc.next();
			char p = sc.next().charAt(0);
			int n = sc.nextInt();
			if (p == '(') {
				if (num == 0) {
					num = n;
					lr = 1;
				} else {
					if (lr > 0) {
						num += n;
					} else {
						if (num >= n) {
							num -= n;
						} else {
							num = n - num;
							lr = 1;
						}
					}
				}
			} else {
				if (num == 0) {
					num = n;
					lr = -1;
				} else {
					if (lr < 0) {
						num += n;
					} else {
						if (num >= n) {
							num -= n;
						} else {
							num = n - num;
							lr = -1;
						}
					}
				}
			}
			if (num == 0)
				out.println("Yes");
			else 
				out.println("No");
		}
	}
	
	public static void main(String[] args) {
		new Main().run();
	}

}