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
Write a program which
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 k-th bracket by the opposite.
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 i-th 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.)
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