Frank is stranded on an island. Everyone else on the island is either a knight or a knave. Knights always tell the truth and liars always lie, but there's no way to tell them apart by appearance.

Five natives (call them A, B, C, D, and E) come up to Frank.

A says: B is a liar.
B says: D is a liar.
C says: B and D are both liars.
D says: E is a liar.
E says: There are even number of knights in this group.

Work out the identities of A, B, C, D, and E from the above statements.