I Believe I Am Mad

Logic Level 4

Edgar Abercombie reached an island where some of the inhabitants are totally mad, and all their beliefs are wrong! The other inhabitants, who are sane, are accurate in their judgments; all their beliefs are correct.

Everyone is completely truthful. Since a mad person believes (wrongly) that he is sane, he will tell you "I am sane".

Which inhabitants can say "I believe I am mad"?

This problem is taken from Raymond M. Smullyan's book Logical Labyrinths.

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