403530: GYM101191 C Ancient CBS

During excavations in one of the caves archaeologists were discovered ancient inscriptions. Each of the records found was a certain number N and correct bracket sequence (CBS).

Recall that the CBS can be defined as follows:

• empty string is the CBS;
• if S is a CBS, then (S) is also a CBS;
• if S₁ and S₂ are CBS, then S₁S₂ is the CBS.

According to some of the records, archaeologists realized that the first number is the number of substrings in the CBS, which are also the CBS. This led archaeologists to believe that if they restore the remaining inscriptions, they will be available for some secret knowledge. Since the walls of the cave mainly found numbers, then they believe that the recovery of the missing CBS possible. The researchers also found that the length of each of the CBS should not exceed 10⁵ characters, because it can not fit on the wall in the cave.

Accordingly, now they need to build such a CBS, which contains exactly N substrings, which are also the CBS.

Single line contains a positive integer N — the number of substring in the CBS, which are also CBS (1 ≤ N ≤ 10⁹).

CBS, which contains exactly N substring being CBS. The length of the output string must not exceed 10⁵ characters.

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