Note that the underscore character is part of the alphabet and will also be encrypted. A key in this scheme consists of 4 digits, each from 0 to 9. Each digit tells how much to shift one character, that is, change it to the character that many positions later in the alphabet. If the shift goes past '_', then we wrap around to the beginning.

The key is applied separately to each group of 4 letters in the message. For example, if the message HI_SALLY is encrypted with the key 2407, the H would be shifted by 2, the I by 4, the underscore by 0, and the S by 7. Then we would start over with the first digit of the key, shifting A by 2, L by 4, and so on. So the ciphertext would be: JM_ZCPLE.

a. Say you obtain a ciphertext of an English sentence encrypted with an unknown key using the scheme. For a brute-force attack, what is the maximum number of keys would you have to test?