Day of the week of an ambiguous date Goal

Write a program or function that returns the day of the week for a date, eg.

01/06/2020  -&gt;  Mon


However, it's unknown if the date is in the format mm/dd/yyyy or dd/mm/yyyy.  If you can be certain of the day of the week, return it.  If there is uncertainty, return an error.

02/07/2020  -&gt;  Err  (Thu? Fri?)


Input

A date in the format #/#/####.


The numbers can optionally have leading zeros.
The year should be read verbatim, assume that 19 = 19 AD, not 19 = 2019 AD.
The separators can be any non-digit character.
Assume the input date is valid in at least one format (ie. not 13/13/2020).
At a minimum, support dates from 2000 through 2030 (which are likely covered by any modern OS and language with a date library.)


Requirements


If the first and second numbers:


are the same (03/03/2020), the date is unambiguous.
either is greater than 12 (13/09/2020, 09/13/2020), the date is unambiguous.
are different and both 12 or less (09/11/2020), the date is ambiguous.



Output


If the date is unambiguous, return the day of the week.
If the date is ambiguous:


If both versions of the date have the same day of the week, return the day of the week.
If both versions of the date have a different day of the week, return an error.

A day of the week should be returned as a string of the day's three-letter abbreviation ("Mon"), case-insensitive.
An error should be returned as any other three-character string, not all whitespace, eg. "Err", "NaN", "???".


Test Cases

02/07/2020  -&gt;  Err
01/06/2020  -&gt;  Mon
05/05/2020  -&gt;  Tue
24/06/2020  -&gt;  Wed
05/09/2030  -&gt;  Thu
03/13/2020  -&gt;  Fri
29/02/2020  -&gt;  Sat
03/12/2000  -&gt;  Sun


Scoring

The code with the least byte count in a week wins the tick.
Bash + GNU utilities, 97 96 93 85 80 76 73 58 56 51 bytes



(${d=date +%a -d$3-}$1-$2;$d$2-$1)|uniq|sed N\;cErr


Try it online!

5 bytes off thanks to user41805, who pointed out that I could use sed's c command instead of the final s command.

2 bytes off thanks to Nahuel Fouilleul. (Nahuel also helped by shaving 4 bytes off in an earlier version that has since been revamped.)

When I noticed that the separators can be any non-digit character, I changed the code to use spaces as the separator. 

This is called with a command like

checkdate 01 06 2020

The output is on stdout.  (There's spurious output on stderr.)