Problem Statement

Find one tuple of $N$ strings $(S_1, S_2 , \dots , S_N)$ that satisfies all of the following conditions.

• $S_i$ consists of (, ).
• $|S_i| \geq 1$
• $|S_1|+|S_2|+\dots + |S_N| \leq N^2$
• There exists exactly $1$ permutation $P=(P_1, P_2, \dots, P_N)$ of $(1,2, \dots, N)$ that satisfies the following.
• $S_{P_1} + S_{P_2} + \dots + S_{P_N}$ is a balanced bracket string.

Here, "$+$" on strings simply denotes string concatenation.

A balanced bracket string is defined as a string that satisfies one of the following conditions.

• The empty string
• A string obtained by concatenating $s,t$ in this order, where there exist non-empty balanced bracket strings $s,t$
• A string obtained by concatenating (, $s$, ) in this order, where there exists a balanced bracket string $s$

Input

$N$

• $2 \leq N \leq 8$
• $N$ is an integer

Output

Print $S_i$ on the $i$-th line.
If there are multiple solutions satisfying the conditions, any of them will be accepted.

Sample

2

)
(()