Time Limit: 2000 MS Memory Limit: 65536 K


Description

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 [({})], [](){}, [{}]()[{}] 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

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

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

Sample Input

6 ()()() 10 (?([?)]?}? 16 ???[???????]????

Sample Output

1 3 92202

Source

SCU 2009 warmup contest 1 ( Happy Birthday to zxhy2 ! )