COCI 2007/2008, Contest #1

Task 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.

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.

Examples

6
()()()

1

10
(?([?)]?}?

3

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

92202

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

All Submissions
Best Solutions

Point Value: 17
Time Limit: 1.00s
Memory Limit: 32M
Added: Aug 13, 2013

Languages Allowed:
C++03, PAS, C, HASK, ASM, RUBY, PYTH2, JAVA, PHP, SCM, CAML, PERL, C#, C++11, PYTH3

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