Consider the set $x=\{SUN,$MON,TUE,WED,THU,FRI,SAT$\}.$ Let $f$ be a function $f$:$xY$

by $f(x)=$ "the number of elements in $x$ that share a letter with $x,$ not including itself." $($For

example, we would not say SUN shares a letter with SUN.$)$

Draw an undirected edge$-$vertex graph representing which elements share a letter.

What is the largest set of numbers could $Y$ be for $f$ to be an onto function?