Longest Balanced Bracket Run

A string of round brackets is balanced when every opening bracket is closed later by its own closing bracket, like "(())()". Given a string s made only of ( and ) that may not be balanced, write longest_balanced(s) that returns the length of its longest balanced substring (a run of consecutive characters). Return 0 if there is none.

Examples

longest_balanced("(()")        # returns 2
longest_balanced(")(()())((")  # returns 6
longest_balanced("())(())")    # returns 4
longest_balanced("))((")       # returns 0

In the second example the run "(()())" in the middle is balanced.

Constraints

• 0 <= len(s) <= 100000
• s holds only the characters ( and ).