CF1574A.Regular Bracket Sequences

普及/提高-

通过率：0%

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题目描述

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 $2n$ .

输入格式

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 $n$ ( $1 \le n \le 50$ ).

输出格式

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.

输入输出样例

输入#1

输出#1

()()()
((()))
(()())
()
((()))
(())()
()(())

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