You are given a bracket string (s) of length (n). You can apply the following operations arbitrary number of times (possibly, zero) and in any order: Choose an index (1 \leq i < |s|) such that (s_i = s_{i+1} = (), and replace both (s_i) and (s_{i+1}) with ()). Choose an index (1 \leq i < |s|) such that (s_i = s_{i+1} = )), and replace both (s_i) and (s_{i+1}) with ((). Find a regular bracket sequence(^{\text{∗}}) (t) which can be obtained from (s) by applying the operations described above, or print (-1) if there is no such (t). (^{\text{∗}})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: the bracket sequences "()()" and "(())" are regular (the resulting expressions are: "(1)+(1)" and "((1+1)+1)") ; the bracket sequences ")(" , "(" and ")" are not. Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^4)). The description of the test cases follows. The first line contains one integer (n) ((1 \leq n \leq 2 \cdot 10^5)) — the length of the string. The second line contains a single string (s) — a sequence of the characters ( and ) of length (n). It is guaranteed that the sum of (n) over all test cases does not exceed (2 \cdot 10^5). For each test case output a regular bracket string (t) which can be obtained from (s) or print (-1) if there is no such (t). In the first testcase, the string "()()" is already a regular bracket sequence. No changes needed. In the second and third testcases it's impossible to reach a regular bracket string from (s). In the fourth testcase we can do the following: "))))))))" (\xrightarrow{i = 1}) "(())))))" "(())))))" (\xrightarrow{i = 5}) "(())(())" .