Bessie and Elsie are plotting to overthrow Farmer John at last! They plan it out over $N (1≤N≤2⋅10^5)$ text messages. Their conversation can be represented by a string $S$ of length $N$ where $S_i$ is either Bor 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.

4
BEEF

2
1
2

9
FEBFEBFEB

2
2
3

10
BFFFFFEBFE

3
2
4
6

SCORING:

• Inputs 4-8: N≤10
• Inputs 9-20: No additional constraints.