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There's More Than One Way To Do It.
Here's a more idiomatic solution using a hyperoperator to compare all the characters to a backslash (which is between the brackets in ASCII), a triangle reduction to return the running sum, a given
to make that list the topic, and then a topicalized junction and a topicalized subscript to test the criteria for balance.
Of course, a Perl 5 programmer might just remove as many inner balanced pairs as possible and then see what's left.