import re
 
def remove_parentheses(s):
    s = s.replace('()', '')  # Bonus!
    opens = [m.start() for m in re.finditer(r'\(', s)]
    closes = [m.start() for m in re.finditer(r'\)', s)]
    pairs = []
    while opens:
        open = opens.pop()
        close = [c for c in closes if c > open][0]
        closes.remove(close)
        pairs.append((open, close))
    nested = sorted([(a, b) for a, b in pairs if (a + 1, b - 1) in pairs])
    while nested:
        open, close = nested.pop()
        s = s[:open] + s[open + 1:close] + s[close + 1:]
        nested = [(a, b if b < close else b - 2) for a, b in nested]
    return s or 'NULL'
 
 
print(remove_parentheses('((a((bc)(de)))f)'))
print(remove_parentheses('(((zbcd)(((e)fg))))'))
print(remove_parentheses('ab((c))'))
print(remove_parentheses('()'))
print(remove_parentheses('((fgh()()()))'))
print(remove_parentheses('()(abc())'))

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