You must correctly solve this problem multiple times to receive full credit.

Consider the language

$L=\{0^{n^2}|n0\}$

A fooling set for $L$ is

$F=\{0^{n^2}|n0\}$

We've picked two distinct strings from the fooling set: $0^{81}$ and $0^{36}.$ Give a distinguishing suffix for these two

strings. $($If your distinguishing suffix is $,$ type $"$e$".$ You may also type $"0^{{?}^{{?}^{?}}}\{n\}"$ or $"1^{{?}^{?}}\{n\}"$ to repeat $0$ or $1n$

times, respectively.$)$

$($Note that for a fooling set question on a written homework or exam, you need to be able to distinguish all

pairs in your proof. To give you some practice on concrete examples, we are only asking you to distinguish

specific pairs for this exercise.$)$