36. Cryptography 3

Solve Cryptography 1 first.

Now suppose that before the text in Cryptography 1 is given to you, it was ciphered using a ROT-$k$ algorithm with the alphabet taken cyclicly but the $k$ is unknown to you. Design an algorithm which, after observing $n$ ciphertext letters, identifies the language $\Upsilon$ or $\Phi$ with the highest possible probability of correctness.