A. Regular Bracket Sequencestime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputA 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.InputThe 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).OutputFor 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.ExampleInput
3
3
1
3
Output
()()()
((()))
(()())
()
((()))
(())()
()(())

3
3
1
3

()()() ((())) (()()) () ((())) (())() ()(()) 
['constructive algorithms', '*800']