Sorry I was unclear. I meant:
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Users will be allowed to sign up in two ways: We either invite them (where they provide the usual email and password), or they sign up via Twitter. We don’t want them to sign up without a twitter account unless we invite them.
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Users are then allowed to sign in either with an email/username & password (if they were invited, and thus set their own password), or sign in with Twitter (if they have an associated account).
Hope that makes it clearer. Thanks.