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BIG-Bench Extra Hard (BBEH) / You are an expert in word sorting. You will be provided with a list of words and…

Problem

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input

You are an expert in word sorting. You will be provided with a list of words and the steps taken, in the form of thoughts, to arrange them in alphabetical order.
Your job is to identify the first step that was a mistake in reasoning about the order of the words. This can be misunderstanding the order of
the alphabet or getting the word or letter wrong or missing a word entirely.
Q: Sort the following words alphabetically: List: appliance addict cardiology nichrome rhesus you're worth merrimack sora dimorphism forfend degrease mallory inveigle cancer slivery informant rickets
Thought 1: I should start by looking at the first letter of the words in the list. The first letter: "appliance": "a" (1). "addict": "a" (1). "cardiology": "c" (3). "nichrome": "n" (14). "rhesus": "r" (18). "you're": "y" (25). "worth": "w" (23). "merrimack": "m" (13). "sora": "s" (19). "dimorphism": "d" (4). "forfend": "f" (6). "degrease": "d" (4). "mallory": "m" (13). "inveigle": "i" (9). "cancer": "c" (3). "slivery": "s" (19). "informant": "i" (9). "rickets": "r" (18).
Thought 2: We now have: (1) ["addict" ? "appliance"] < (3) ["cardiology" ? "cancer"] < (4) ["degrease" ? "dimorphism"] < (6) "forfend" < (9) ["informant" ? "inveigle"] < (13) ["mallory" ? "merrimack"] < (14) "nichrome" < (18) ["rhesus" ? "rickets"] < (19) ["sora" ? "slivery"] < (23) "worth" < (25) "you're".
Thought 3: Now let's sort this subpart ["addict" ? "appliance"] by looking at their second letters. The second letter: "addict": "d" (4). "appliance": "p" (16).
Thought 4: We now have: (4) "addict" < (16) "appliance" for the subpart. Hence, we have "addict" < "appliance" < ["cardiology" ? "cancer"] < ["degrease" ? "dimorphism"] < "forfend" < ["informant" ? "inveigle"] < ["mallory" ? "merrimack"] < "nichrome" < ["rhesus" ? "rickets"] < ["sora" ? "slivery"] < "worth" < "you're".
Thought 5: Now let's sort this subpart ["cardiology" ? "cancer"] by looking at their second letters. The second letter: "cardiology": "a" (1). "cancer": "a" (1).
Thought 6: We now have: (1) ["cardiology" ? "cancer"] for the subpart. Hence, we have "addict" < "appliance" < ["cardiology" ? "cancer"] < ["degrease" ? "dimorphism"] < "forfend" < ["informant" ? "inveigle"] < ["mallory" ? "merrimack"] < "nichrome" < ["rhesus" ? "rickets"] < ["sora" ? "slivery"] < "worth" < "you're".
Thought 7: Now let's sort this subpart ["degrease" ? "dimorphism"] by looking at their second letters. The second letter: "degrease": "r" (18). "dimorphism": "i" (9).
Thought 8: We now have: (9) "dimorphism" < (18) "degrease" for the subpart. Hence, we have "addict" < "appliance" < ["cardiology" ? "cancer"] < "dimorphism" < "degrease" < "forfend" < ["informant" ? "inveigle"] < ["mallory" ? "merrimack"] < "nichrome" < ["rhesus" ? "rickets"] < ["sora" ? "slivery"] < "worth" < "you're".
Thought 9: Now let's sort this subpart ["informant" ? "inveigle"] by looking at their second letters. The second letter: "informant": "n" (14). "inveigle": "e" (5).
Thought 10: We now have: (5) "inveigle" < (14) "informant" for the subpart. Hence, we have "addict" < "appliance" < ["cardiology" ? "cancer"] < "dimorphism" < "degrease" < "forfend" < "inveigle" < "informant" < ["mallory" ? "merrimack"] < "nichrome" < ["rhesus" ? "rickets"] < ["sora" ? "slivery"] < "worth" < "you're".
Thought 11: Now let's sort this subpart ["mallory" ? "merrimack"] by looking at their second letters. The second letter: "mallory": "a" (1). "merrimack": "e" (5).
Thought 12: We now have: (1) "mallory" < (5) "merrimack" for the subpart. Hence, we have "addict" < "appliance" < ["cardiology" ? "cancer"] < "dimorphism" < "degrease" < "forfend" < "inveigle" < "informant" < "mallory" < "merrimack" < "nichrome" < ["rhesus" ? "rickets"] < ["sora" ? "slivery"] < "worth" < "you're".
Thought 13: Now let's sort this subpart ["rhesus" ? "rickets"] by looking at their second letters. The second letter: "rhesus": "e" (5). "rickets": "i" (9).
Thought 14: We now have: (5) "rhesus" < (9) "rickets" for the subpart. Hence, we have "addict" < "appliance" < ["cardiology" ? "cancer"] < "dimorphism" < "degrease" < "forfend" < "inveigle" < "informant" < "mallory" < "merrimack" < "nichrome" < "rhesus" < "rickets" < ["sora" ? "slivery"] < "worth" < "you're".
Thought 15: Now let's sort this subpart ["sora" ? "slivery"] by looking at their second letters. The second letter: "sora": "o" (15). "slivery": "l" (12).
Thought 16: We now have: (12) "slivery" < (15) "sora" for the subpart. Hence, we have "addict" < "appliance" < ["cardiology" ? "cancer"] < "dimorphism" < "degrease" < "forfend" < "inveigle" < "informant" < "mallory" < "merrimack" < "nichrome" < "rhesus" < "rickets" < "slivery" < "sora" < "worth" < "you're".
Thought 17: I have now sorted all the words. The answer is addict appliance cardiology cancer degrease dimorphism forfend informant inveigle mallory merrimack nichrome rhesus slivery rickets sora worth you're
Q: Is there a mistake in this sequence? Write "No" if there are no mistakes, or the number N if there is a mistake in Thought N.

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