Word about crime and Agatha Christie

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Across
  1. 1. search
  2. 4. clue
  3. 6. detective
  4. 8. mystery
  5. 9. a scenario
  6. 10. to talk and being suspect
  7. 13. to become interested
  8. 14. scary movie
  9. 15. herring
  10. 17. kill
  11. 18. to have an idea
  12. 19. interrogation
  13. 20. to find the missing piece
Down
  1. 2. to verify that someone doesn't
  2. 3. interrogation
  3. 5. to have a stress ending
  4. 7. enigma
  5. 11. to find
  6. 12. judge
  7. 16. hercule poirot