How would you back up a 300 TB database?

I got stumped by a question that I got while on the road this week, and I thought I’d throw it out.  A user came up to me who has a 300 TB Oracle database that generates 3-4 TB of transaction logs a day.  They are currently unable to back it up — at all.  When I suggested my usual, she shocked me and said that they had tried it.  Ouch.
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