B'A regular bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters '1 ' and '+ ' between the original characters of the sequence. For example: Let 's define the inverse of the bracket sequence as follows: replace all brackets '( ' with ') ', and vice versa (all brackets ') ' with '( '). For example, strings "()((" and ")())" are inverses of each other. You are given a regular bracket sequence s . Calculate the number of pairs of integers (l,r) ( 1 <= l <= r <= |s| ) such that if you replace the substring of s from the l -th character to the r -th character (inclusive) with its inverse, s will still be a regular bracket sequence. The first line contains a single integer t ( 1 <= t <= 10^4 ) -- the number of test cases. The only line of each test case contains a non-empty regular bracket sequence; it consists only of characters '( ' and/or ') '. Additional constraint on the input: the total length of the regular bracket sequences over all test cases doesn 't exceed 2 cdot 10^5 . For each test case, print a single integer -- the number of pairs (l,r) meeting the conditions from the statement. In the first example, there is only one pair: In the second example, there are no pairs. In the third example, there are three pairs: '...