Find the Wavy Words! (Note: this is an easier spin-off of my previous challenge Find the Infinity Words!, which is a spin-off of my other previous challenge Find the Swirling Words! :) )

Definition of a Wavy Word:


If you connect with curves all the characters of a Wavy Word on the alphabet (A-Z) you obtain the path of a wave continuously going toward right or toward left and never changing direction, like in the diagrams below.
A Wavy Word can be:


Raising if each consecutive character is at the right (on the alphabet) of the previous one.
Decreasing if each consecutive character is at the left (on the alphabet) of the previous one.

All the even connection must be down, all the odd connections must be up.
You can ignore upper/lowercase or consider/convert all to upper case or all to lower case.
The input words are only characters in the alphabet range of A-Z, no spaces, no punctuation, or symbols.
If a word has double characters, like "SPOON", you must collapse the doubles to one character: "SPOON" > "SPON" (because if you go from O to O is zero distance).
The Wavy Words will contain at least 3 distinct characters (even after doubles collapsing).


Here there are some examples:



Task:

Write a full program or function that will take a word from standard input and will output if it is a Wavy Word or not, and in positive case, output if it is raising or decreasing. The output can be True/False/Null, 2/1/0, 1/Null/0, -1/0/1, NO/WR/WD, etc, you decide how to represent it.

Test cases:

WAVY WORDS:
  ADEPT, BEGIN, BILL, BOSS, BOOST, CHIMP,
  KNOW, SPONGE, SPOON, TROLL, WOLF  

ADEPT  &gt; YES &gt; RAISING
BEGIN  &gt; YES &gt; RAISING
BILL   &gt; YES &gt; RAISING
BOSS   &gt; YES &gt; RAISING
BOOST  &gt; YES &gt; RAISING
CHIMP  &gt; YES &gt; RAISING
KNOW   &gt; YES &gt; RAISING
SPONGE &gt; YES &gt; DECREASING
SPOON  &gt; YES &gt; DECREASING
TROLL  &gt; YES &gt; DECREASING
WOLF   &gt; YES &gt; DECREASING

NOT WAVY WORDS:
  WATCH, EARTH, NINON, FOO, BAR, WAVE, SELECTION,
  YES, NO, DEFINITION, WATER, WINE, CODE, AAAHHHH, I, MM, ABCA


Rules:


Shortest code wins.


Optional Task:

Find, as a list, as many Wavy Words as you can in an English dictionary, and the longest as well. You can take for example as reference the complete list of English words here.
05AB1E, 11 9 bytes (Thanks to Adnan)

Dg2›iÇü‹Ù


Try it online!

Wavy Cases:

0 - Decreasing Wavy  

1 - Increasing Wavy 

Not Wavy Cases:

[0,1] - Not wavy, initially decreasing, but then has an increase/equality that broke the pattern.  

[1,0] - Not wavy, initially increasing, but then has a decrease/equality that broke the pattern  

Input String - Not possible to be wavy in the first place due to length.

Explanation:

Dg2›iÇü‹Ù   # Full program

D           # Push 2 copies of input.
 g2›i       # If length is greater than 2. 
     Ç      # Push ASCII values for all characters in the string.
      ü     # Push pairwise array.
       ‹    # Vectorize 1 if negative difference, 0 if positive difference.
        Ù   # Uniquify using right most unique values first.
            # Else just print the string back, letting them know it's not valid input.