Let's say we have $7$ elements $($numbered $0$ to $6).$ Are the following arrays legal

id$-$arrays in Union$-$Finnd? Justify! For those that are legal, they may have come up in

the weighted quick$-$union algorithm? Draw the trees in all cases and explain why each of the arrays can come up in Quick$-$union, or show a sequence of union operations which end in this array.

a$.3,5,6,3,3,2,2$

b$.0,2,2,2,0,2,2$

c$.4,0,2,0,4,4,3$