Balanced Brackets Queries

Given a string A of length N consists of only ’(‘ and ’)’. Answer M queries (L, R), find the length of the maximum correct bracket subsequence of sequence A_L , A_{L + 1} , … , A_R.

Note: A sequence T is a subsequence of A if T can be generated by deleting some elements of A.

Input Format:

    First argument contains the string A
    Second argument contains a M x 2 grid B denoting queries

Output Format:

    return an integer array denoting the answers to the respective queries

Constraints:

    1 <= N,M <= 100000
    1 <= l <= r <= N

For Example:

Input 1:
    A = "())(())(())(" B = [[1, 1], [1, 3], [1, 12], [5,11]]
Output 1:
    [0, 2, 10, 6]
Explanation:
    [1,1] corresponds to "(" which has no correct bracket subsequence.
    [1,3] corresponds to "())" which has "()" as correct bracket subsequence.

NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a doubt? Checkout Sample Codes for more details.