Consider the following cryptosystem:

Let the plaintext and ciphertext space be .  The secret key is , where each for .

To encrypt a string of plaintext symbols using key  , we perform the following operation to obtain ciphertext   :

, if ;

,  if ;

,  if .

In other words, we add (mod 5) to the first position of the plaintext, to the second position of the plaintext, to the third position of the plaintext, and continue with adding to the fourth position of the plaintext, to the fifth position of the plaintext and so forth.

Suppose you intercepted the ciphertext 0 1 4 4 0 0 3 2 1, and you know that the plaintext in positions 4, 8 and 9 are 3, 4, 4, that is, the plaintext is 3   , 4, 4, where indicates that these symbols are unknown.  

Determine the key.