The function is given a string consisting of a collection of three characters:

• "(" open bracket
• ")" closed bracket
• "J" Joker, which can be replaced by "(", ")" or ""

Develop a solution to determine if the given string represents a proper sequence of parenthesis; return true / false. Each open bracket on the left should have a corresponding closed bracket on the right. For example "(()())" is a proper sequence, "()(()" is not a proper sequence. The presence of Jokers adds an extra level of difficulty to the analysis because each "J" makes three possibilities to consider. An empty string is considered a valid string because it does not contain unbalanced brackets.

Examples

closed_brackets("(J))") ➞ true
# J can be replaced with (

closed_brackets("(") ➞ false
# Unbalanced open bracket.

closed_brackets("") ➞ true
# Empty string is a valid sequence.

closed_brackets("()J(") ➞ false
# Not possible to balance the brackets.

closed_brackets("J") ➞ true
# J can be replaced with an empty string.

closed_brackets(")(") ➞ false
# Numbers of ( and ) are the same but they are in the wrong places.

closed_brackets("()") ➞ true
# A proper sequence of balanced brackets.

Notes

N/A