We're all mad here! II

Logic Level 2

Everyone in Wonderland is either sane or mad. A sane person believes a statement if and only if it is true. A mad person believes a statement if and only if it is false.

One day, the Mad Hatter, the March Hare, and the Dormouse had tea. The three were good friends, and all knew whether each of the three were mad or sane (although who knows if they really believed it).

The Mad Hatter said, "I believe that the March Hare and Dormouse are both mad."

The March Hare replied, "I believe that the Dormouse believes the Mad Hatter is sane."

The Dormouse finished, "I believe that the Mad Hatter is sane."

Exactly which of the three are mad?

If you're stuck, try this problem.
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