## USACO 2023 US Open Contest, Bronze

## Problem 1. FEB

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Bessie and Elsie are plotting to overthrow Farmer John at last! They plan it out over $N$ ($1\le N\le 2\cdot 10^5$) 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
$S$.

#### INPUT FORMAT (input arrives from the terminal / stdin):

The first line will consist of one integer $N$.The next line contains $S$.

#### OUTPUT FORMAT (print output to the terminal / stdout):

First output $K$, the number of distinct excitement levels possible. On the next $K$ lines, output the excitement levels, in increasing order.#### SAMPLE INPUT:

4 BEEF

#### SAMPLE OUTPUT:

2 1 2

#### SAMPLE INPUT:

9 FEBFEBFEB

#### SAMPLE OUTPUT:

2 2 3

#### SAMPLE INPUT:

10 BFFFFFEBFE

#### SAMPLE OUTPUT:

3 2 4 6

#### SCORING:

- Inputs 4-8: $N\le 10$
- Inputs 9-20: No additional constraints.

Problem credits: William Yue and Claire Zhang