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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def _find_common_roots(paths):
 """Out of some paths it finds the common roots that need monitoring."""

    paths = [x.split(os.path.sep) for x in paths]
    root = {}
    for chunks in sorted(paths, key=len, reverse=True):
        node = root
        for chunk in chunks:
            node = node.setdefault(chunk, {})
        node.clear()

    rv = set()

    def _walk(node, path):
        for prefix, child in iteritems(node):
            _walk(child, path + (prefix,))
        if not node:
            rv.add("/".join(path))

    _walk(root, ())
    return rv