TOPlap is an international company, with employees from all over the world. The cybersecurity specialist in your office is from Greece. One day after lunch, she left a bunch of papers spread out on the table. Is this a prank? Certainly she would never leave sensitive papers out like that. Intrigued, you take a peek. The texts use the modern Greek alphabet, but as far as you can tell, the words make no sense. Words are strange jumbles of letters, in impossible combinations. Google translate can make no sense of them.
You know that your colleague takes an interest in historical ciphers. On a hunch, you are going to test the theory that these texts may have been obfuscated using Caesar's cipher.
Caesar's cipher works as follows. Take each letter and shift it a certain number of places further down the alphabet. If you shift three places, then A becomes D, B becomes E, etc. The whole alphabet wraps around, so X, Y and Z become A, B and C respectively. To decode a message, the receiver would do the same but in reverse: D becomes A, etc. etc. It is said that Julius Caesar applied this method to keep his communications secret on the battlefield.
It's possible to do the same in Greek. The Greek alphabet has 24 letters. Just like our Latin alphabet, there are upper- and lower-case variants.
ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩ
αβγδεζηθικλμνξοπρστυφχψω
One thing to note, is that there are two lower-case variants of sigma: 'σ' and 'ς'. These represent the same letter - the second form is just an added flourish when the word ends in a sigma. However, to keep things interesting for programmers, they are encoded as separate codepoints. 'σ' is U+03C3 and 'ς' is U+03C2. When shifting to the right, both 'σ' and 'ς' would be encoded as tau 'τ'. To the left, both would be encoded as rho 'ρ'.
Let's continue our guesswork by assuming that some of these texts mention the hero Odysseus (Οδυσσευς). Take for example the following test input:
σζμ γ' ωοωλδθαξλδμξρ οπξρδυζ οξκτλζσθρ Ξγτρρδτρ.
αφτ κ' λαλψφτ ωπφχλρφτ δξησηρζαλψφτ φελο, Φκβωωλβ.
γ βρφαγζ ωνψν ωγφ πγχρρφ δρδαθωραγζ ρφανφ.
If we carefully rotate the first sentence one letter, so α becomes β, β becomes γ, γ becomes δ, etc. etc., we get:
την δ' απαμειβομενος προσεφη πολυμητις Οδυσσευς.
As you can see, the last word of this sentence is indeed the name Odysseus. The second sentence can be decoded as follows after 18 alphabet rotations:
τον δ' ετερον σκοπελον χθαμαλωτερον οψει, Οδυσσευ.
Here, the name Odysseus occurs in a grammatical variant with slightly different spelling. Other variants that may occur are:
Οδυσσευς - Odysseus
Οδυσσεως - Odysseos
Οδυσσει - Odyssei
Οδυσσεα - Odyssea
Οδυσσευ - Odysseu
The third sentence of the test input does not contain a mention of Odysseus, no matter how many times you rotate the alphabet.
Now we can calculate the total sum of alphabet rotations you have to do to reveal all lines mentioning Odysseus (any spelling variant). For the test input above, that sum would be 1 + 18 + 0 = 19 in total.
What is the sum total of alphabet shifts for lines mentioning Odysseus?
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