P9183 [USACO23OPEN] FEB B

Bessie and Elsie are plotting to overthrow Farmer John at last! They plan it out over $N$ text messages. Their conversation can be represented by a string $S$ of length $N$ where $S_i$ is either `B` or `E`, meaning the $i$ th message was sent by Bessie or Elsie, respectively. However, Farmer John hears of the plan and attempts to intercept their conversation. Thus, some letters of $S$ are `F`, meaning Farmer John obfuscated the message and the sender is unknown. The **excitement level** of a non-obfuscated conversation is the number of times a cow double-sends - that is, the number of occurrences of substring `BB` or `EE` in $S$. You want to find the excitement level of the original message, but you don’t know which of Farmer John’s messages were actually Bessie’s / Elsie’s. Over all possibilities, output all possible excitement levels of $S$.

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$1\le N\le 2\cdot 10^5$. - Inputs 4-8: $N\le 10$. - Inputs 9-20: No additional constraints.