John likes simple ciphers. He had been using the "Caesar" cipher to encrypt his diary until recently, when he learned a hard lesson about its strength by catching his sister Mary browsing through the diary without any problems.

Rapidly searching for an alternative, John found a solution: the famous "Autokey" cipher. He uses a version that takes the $$$26$$$ lower-case letters 'a'–'z' and internally translates them in alphabetical order to the numbers $$$0$$$ to $$$25$$$.

The encryption key $$$k$$$ begins with a secret prefix of $$$n$$$ letters. Each of the remaining letters of the key is copied from the letters of the plaintext $$$a$$$, so that $$$k_{n+i} = a_{i}$$$ for $$$i \geq 1$$$. Encryption of the plaintext $$$a$$$ to the ciphertext $$$b$$$ follows the formula $$$b_i = a_i + k_i \bmod 26$$$.

Mary is not easily discouraged. She was able to get a peek at the last $$$n$$$ letters John typed into his diary on the family computer before he noticed her, quickly encrypted the text document with a click, and left. This could be her chance.