A1106. [COCI-2007_2008-contest1]#6 ZAPIS

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.

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.

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

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