Mythical animals

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Across
  1. 3. People belive these litte fliers grant you wishes. One of them collects teeth and gives you some money for them.
  2. 6. It's a mix of fire and a bird who can revive itself from the dead using its burned-out ashes.
  3. 7. It's like a horse with wings.
  4. 9. This is a human-shaped, greedy and green monster
  5. 10. Many people believe this lives in ice-cold caves and is covered with fur.
Down
  1. 1. It's like a horse with a magical horn.
  2. 2. It's a one-eyed giant.
  3. 4. It's a wolf-human shapeshifter
  4. 5. This is a huge fire-breathing lizard.
  5. 8. This is what shrek is called by the locals.