CF1574A Regular Bracket Sequences

A bracket sequence is a string containing only characters "(" and ")". 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, bracket sequences "()()" and "(())" are regular (the resulting expressions are: "(1)+(1)" and "((1+1)+1)"), and ")(", "(" and ")" are not. You are given an integer $ n $ . Your goal is to construct and print exactly $ n $ different regular bracket sequences of length $ 2n $ .

The first line contains one integer $ t $ ( $ 1 \le t \le 50 $ ) — the number of test cases. Each test case consists of one line containing one integer $ n $ ( $ 1 \le n \le 50 $ ).

For each test case, print $ n $ lines, each containing a regular bracket sequence of length exactly $ 2n $ . All bracket sequences you output for a testcase should be different (though they may repeat in different test cases). If there are multiple answers, print any of them. It can be shown that it's always possible.