## COCI '07 Contest 1 #4 Zapis

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Points: 15 (partial)
Time limit: 0.6s
Memory limit: 32M

Problem type

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 [({})], [](){} and [{}]()[{}] 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.

#### Input Specification

The first line contains an even integer , the length of the string.

The second line contains the string. Illegible characters are represented by the ? character.

#### Output Specification

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

#### Sample Input 1

6
()()()

#### Sample Output 1

1

#### Sample Input 2

10
(?([?)]?}?

#### Sample Output 2

3

#### Explanation for Sample Output 2

In the second example, the three matching regular bracket-sequences are ({([()])}), ()([()]{}) and ([([])]{}).

#### Sample Input 3

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

#### Sample Output 3

92202