At each of the vertices of a cube sits a Bunchkin.
Two Bunchkins are said to be adjacent if and only if they sit at either end of one of the cube's edges. Each Bunchkin is either a 'truther', who always tells the truth, or a 'liar', who always lies. All eight Bunchkins say 'I am adjacent to exactly two liars'.
What is the maximum number of Bunchkins who are telling the truth?
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