Here's how it works:
You're given the string "?<???????????)??]???????}??"

The task is to find the number of ways to replace each question mark with one of the characters in the string "()<>[]{}" such that the end result is valid parentheses sequence.

For example:

()[]{}<> is valid

([]()){} is valid

]() is not valid

(]{} is not valid

([)) is not valid.

Here are some test cases:

?[?? has 4 completions.

???? has 32 completions.

)??? has 0 complteions.

More formally validity is defined by:

1. The empty string is valid.

2. If a string S is valid then a+S+b is valid where "+" is string concatenation. And a,b are open/close brackets of identical type.

3. If S_1 and S_2 are valid bracket strings then S_1 + S_2 is a valid bracket string.

Market resolves YES if anyone posts the answer in the comments or NO if market closes before that.

Market closes 7th of april.