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 is a regular bracket-sequence, then , and are also regular bracket-sequences.
- If and are regular bracket-sequences, then 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`

## Comments

Sample input 2 - confusing

How can the output be "(([()]))" when the input contains a "}" character???

Sample input 2: (?([?)]?}?

Also, why is the sample input different length then the output?

Braces were not escaped; issue has been fixed.