BRCKTS  Brackets
We will call a bracket word any word constructed out of two sorts of characters: the opening bracket "(" and the closing bracket ")". Among these words we will distinguish correct bracket expressions. These are such bracket words in which the brackets can be matched into pairs such that
 every pair consists of an opening bracket and a closing bracket appearing further in the bracket word
 for every pair the part of the word between the brackets of this pair has equal number of opening and closing brackets
 replacement  changes the ith bracket into the opposite one
 check  if the word is a correct bracket expression
Task
Write a program which
 reads (from standard input) the bracket word and the sequence of operations performed,
 for every check operation determines if the current bracket word is a correct bracket expression,
 writes out the outcome (to standard output).
Input
Ten test cases (given one under another, you have to process all!). Each of the test cases is a series of lines. The first line of a test consists of a single number n (1<=n<=30000) denoting the length of the bracket word. The second line consists of n brackets, not separated by any spaces. The third line consists of a single number m  the number of operations. Each of the following m lines carries a number k denoting the operation performed. k=0 denotes the check operation, k>0 denotes replacement of kth bracket by the opposite.
Output
For every test case your program should print a line:
Test i:
where i is replaced by the number of the test
and in the following lines, for every check operation in the ith test
your program should print a line with the word
YES,
if the current bracket word is a correct bracket expression, and a line
with a word
NO otherwise.
(There should be as many lines as check operations in the test.)
Example
Input: 4 ()(( 4 4 0 2 0 [and 9 test cases more] Output: Test 1: YES NO [and 9 test cases more]Warning: large Input/Output data, be careful with certain languages
hide comments
Archit Jain:
20140920 20:37:27
very nice q 

Shreyansh Gandhi:
20140622 19:44:56
My 50th :) 

Julian Waldby:
20140521 05:31:49
I think instead of O(n) it is O(mn).


humble_coder:
20140427 15:05:55
any limit on m???


rd:
20131126 11:41:48
Hi


Rajesh Kumar Pal:
20131120 20:18:45
printf is much faster than cout :P :P 

Santiago Palacio:
20130130 05:42:08
For c++... i highly recommend NOT USING string, use char [] and scanf. 

nitish25:
20130119 23:08:36
is this ())(() correct bracket expression?


YangYue:
20121206 11:29:23
Is there a O(n) way to solve this problem?


PengFei Du:
20150104 11:19:38
O(n) is truth that can get TLE.

Added by:  Adam Dzedzej 
Date:  20040615 
Time limit:  11s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL6 VB.NET 
Resource:  Internet Contest Pogromcy Algorytmow(Algorithm Tamers) 2003 Round IV 