2024 AIME II Problem 2

A list of positive integers has the following properties:

• The sum of the items in the list is 30.

• The unique mode of the list is 9.

• The median of the list is a positive integer that does not appear in the list itself.

Find the sum of the squares of all the items in the list.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.