Regular Bracket Sequences

题意翻译

一个字符串是括号序列仅当其仅包含 `(` 和 `)` 字符。 定义合法括号序列如下： - 不是括号序列的字符串也不是合法括号序列。 - 空字符串是合法括号序列。 - 如果 `s,t` 均为合法括号序列，那么 `st` 也是合法括号序列。 - 如果 `s` 是合法括号序列，那么 `(s)` 也是合法括号序列。 给定整数 $n$，构造 $n$ 个长度为 $2\times n$ 且互不相同的合法括号序列。 $T$ 组数据，保证有解。 保证： $1\leq T\leq 50;1\leq n\leq 50;$

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 $ .

输入输出格式

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

输入样例 #1

3
3
1
3

输出样例 #1

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