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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 verify(self, payload):
 """ Verify payload authenticity via the supplied authenticator """

        if not self.authenticator:
            return payload
        try:
            self.authenticator.auth(payload)
            return self.authenticator.unsigned(payload)
        except AuthenticatorInvalidSignature:
            raise
        except Exception as exception:
            raise AuthenticateError(str(exception))