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def isvalid(s):
        ctr = 0
        for c in s:
            if c == '(':
                ctr += 1
            elif c == ')':
                ctr -= 1
                if ctr < 0:
                    return False
        return ctr == 0
    level = {s}
    while True:
        # removfe items in level which are not valid
        valid = filter(isvalid, level)