Design a TM$,$ deterministic or nondeterministic, for

L $=\{$w: n$\_($a$)($w$)=$ n$\_($b$)($w$)=$ n$\_($c$)($w$)\},=\{$a$,$ b$,$ c$\}.$

Note: $($The underscore is supposed to be subscript for a$,$ b$,$ and c$.$ The $($w$)$ is not$)$

You may use as many track tapes as needed. You may use the stay option, in addition to left and right.

Give:

$1.$ the algorithm used

$2.$ image of the JFLAP TM including each states' meaning using the "Change Label" option

$3.$ Show image of at least $10$ test cases in JFLAP $($good and bad$)$ to fully prove that TM is functional

$4.$ explain if and how nondeterminism simplifies the task

$5.$ a description of whether your TM works or not, if not, to what extent.