facetime doesn't accept correct password
Hello,
My iPhone 4 has been updated to iOS6 and everything looks okay.
Whenever I am prompt to use my apple id password I do and everything looks okay.
Messages are working okay with my apple id and phone number, but facetime doesn't accept my apple id password saying that is wrong.
What can I do about it? Without signing in to my apple id I can accept facetime calls only on my phone number.
Please advice.
Thanks.
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A.
MacBook Pro, OS X Mountain Lion