문제

A regular bracket-sequence is a string of characters consisting only of opening and closing brackets, and satisfying the following conditions:

• An empty string is a regular bracket-sequence.

• If A is a regular bracket-sequence, then (A), [A] and {A} are also regular bracket-sequences.

• If A and B are regular bracket-sequences, then AB is also a regular bracket-sequence.

For example, the sequences [({})], {} i {}[{}] are regular, but the sequences [({{([, } and [{}])([{}] are not. Ivica has found a string which looks like it could be a regular bracket-sequence. Some of the characters have become smudged and illegible, and could have been any character. Write a program that calculates how many ways the illegible characters in the string can be replaced by brackets so that the result is a regular bracket-sequence. This number can be very large, so output only its last 5 digits.

입력

The first line contains an even integer N (2 ≤ N ≤ 200), the length of the string. The second line contains the string. Illegible characters are represented by the '?' character.

출력

Output the number of regular bracket-sequences the string could have read.

예제 입력 1

6
()()()

예제 출력 1

1

예제 입력 2

10
(?([?)]?}?

예제 출력 2

3

예제 입력 3

16
???[???????]????

예제 출력 3

92202