Just the MaDaM

There is a 9x9 array of the letter M, A and D in this puzzle. The arrangement starts from the middlemost grid (at the (5,5) position) with a single M, surrounded by eight A's, which in turn surrounded by 16 D's, then 24 A's and lastly 32 M's as the outermost "ring". Now that we have in total 33 M, 32 A and 16 D arranged symmetrically, how many ways are there that the word MADAM can be "written" by following the allowable movement on the given array?
Allowable movement : from original letter position to any of its 8 neighboring (surrounding) positions, wherever possible. You can start from and end up anywhere there is an M. And even though MADAM is a palindrome, in this puzzle here direction matters.
Credit goes to Milan Milanic who wrote part One and Two of this question. Thank you.

Remember that there is only one rule, the next letter must be a neighbor. Direction matters.