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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 nn… Your goal is to construct and print exactlynn different regular bracket sequences of length n2n

### Regular Bracket Sequences solution codeforces

The first line contains one integer tt (≤ ≤ 501t50) – the number of test cases.

Each test case consists of one line containing one integer nn (≤ ≤ 501n50).

### Regular Bracket Sequences solution codeforces

For each test case, print nnlines, each containing a regular bracket sequence of length exactlyn2n… 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.

Example
input

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3
3
1
3


### Regular Bracket Sequences solution codeforces

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