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: A bracket sequence is called beautiful if one of the following conditions is satisfied: For example, the bracket sequences "()()", "(())", ")))(((", "))()((" are beautiful. You are given a bracket sequence s . You have to color it in such a way that: Color the given bracket sequence s into the minimum number of colors according to these constraints, or report that it is impossible. The first line contains one integer t ( 1 <= t <= 10^4 ) -- the number of test cases. Each test case consists of two lines. The first line contains one integer n ( 2 <= n <= 2 cdot 10^5 ) -- the number of characters in s . The second line contains s -- a string of n characters, where each character is either "(" or ")". Additional constraint on the input: the sum of n over all test cases does not exceed 2 cdot 10^5 . For each test case, print the answer as follows: '...