Consider the following statements regarding the origin and development of Mohiniyattam:
Mohiniyattam derives its name from Mohini, the female form of Lord Vishnu.

1. It originated exclusively from the Devadasi system of Tamil Nadu.
2. It was patronised and codified by Swathi Thirunal, King of Travancore.
3. Palakkad Parameshwara Bhagavathar played a role in spreading the art form to central Kerala.

Which of the above statements are correct?