I had a similar problem sometime back and found BidiMap from Apache Commons. However, you might have to add the same SSN multiple times for each bank account.
The first String is the account number. That is because the account number is unique. The second String will be the SSN. That is because each account number has one and only one SSN, but there can be more than one account associated with each SSN. The API for Map provides lots of ways of searching by value or by key, so you will be able to output in many ways.
When you do things right, people won't be sure you've done anything at all.
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