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

The first line contains an even integer ~N (2 \leq N \leq 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.

Input Sample #1

6 ()()()

Output Sample #1

1

Input Sample #2

10 (?([?)]?}?

Output Sample #2

3

Input Sample #3

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

Output Sample #3

92202

Hint

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