Problem:
Score : 400 points

Problem Statement

Snuke has N strings. The i-th string is s_i.

Let us concatenate these strings into one string after arranging them in some order.
Find the maximum possible number of occurrences of AB in the resulting string.

Constraints

1 \leq N \leq 10^{4}

2 \leq |s_i| \leq 10

s_i consists of uppercase English letters.

Input

Input is given from Standard Input in the following format:

N
s_1
\vdots
s_N

Output

Print the answer.

Sample Input 1

3
ABCA
XBAZ
BAD

Sample Output 1

2

For example, if we concatenate ABCA, BAD and XBAZ in this order, the resulting string ABCABADXBAZ has two occurrences of AB.

Sample Input 2

9
BEWPVCRWH
ZZNQYIJX
BAVREA
PA
HJMYITEOX
BCJHMRMNK
BP
QVFABZ
PRGKSPUNA

Sample Output 2

4

Sample Input 3

7
RABYBBE
JOZ
BMHQUVA
BPA
ISU
MCMABAOBHZ
SZMEHMA

Sample Output 3

4

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Control.Monad

readIntLine :: IO ([Int])
readIntLine = do
    x <- getLine
    return $ map (read :: String -> Int) $ words x

main :: IO ()
main = do
    [n] <- readIntLine
    lines <- replicateM n getLine
    solve lines

solve lines =
    let inner = sum $ map countAB lines
        outer1 = (length $ filter (('A'==). last) lines)
        outer2 = (length $ filter (('B'==). head) lines)
        outer = min outer1 outer2
        yonder = if (length $ filter (\l -> (('A'==). last) l && (('B'==). head) l) lines) == (max outer1 outer2) && outer > 0 then 1
                                                                                                                               else 0
      in print $ inner + outer - yonder

countAB [] = 0
countAB [x] = 0
countAB ('A':'B':xs) = 1 + countAB xs
countAB (x:xs) = countAB xs