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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 add_proxy_auth(possible_proxy_url, proxy_auth):
 """ Add a username and password to a proxy URL, if the input value is a proxy URL. :param str possible_proxy_url: Proxy URL or ``DIRECT``. :param requests.auth.HTTPProxyAuth proxy_auth: Proxy authentication info. :returns: Proxy URL with auth info added, or ``DIRECT``. :rtype: str """

    if possible_proxy_url == 'DIRECT':
        return possible_proxy_url
    parsed = urlparse(possible_proxy_url)
    return '{0}://{1}:{2}@{3}'.format(parsed.scheme, proxy_auth.username, proxy_auth.password, parsed.netloc)