Here, have some copium

Progress:

• Proved the l = n - 1 case

• Conjectured a closed form for the answer (which is correct: (l-1)^2/(n(n-1)) + 1/n)

• Proved that we can assume all A_i are distinct

• Provided the construction for the conjectured answer, but did not have time to finish proving the construction works

• Said the word "Jensen" which probably doesn't work anyway lol

Resolves N/A if MAA is extra goofy and doesn't release score distributions

edit: turns out you ahve to do some substitution so this is looking unlikely but if maa is really nice on partials like last year (i only wrote the answer, in fact a wrong answer, for usamo3, with a few ideas, and got 2 points) it's still plausible, i doubt it though