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: Wrong Answer)

import Control.Applicative
import Control.Monad
import Data.List
type I3 = (Int, Int, Int)
type B2 = (Bool, Bool)

main :: IO ()
main = do
    n <- readLn
    ss <- replicateM n getLine
    print . f $ map count ss

f :: [(I3, Int)] -> Int
f rs = sum ns + g (nft, ntf, ntt) where
    (cs, ns) = unzip rs
    (nft, ntf, ntt) = foldl1 add3 cs

g :: I3 -> Int
g (nft, ntf, 0) = min nft ntf
g (nft, ntf, ntt) = min nft ntf + (ntt - 1) + rem where
    rem = if nft == ntf then 0 else 1

add3 :: I3 -> I3 -> I3
add3 (l1,l2,l3) (r1,r2,r3) = (l1+r1,l2+r2,l3+r3)

classify :: B2 -> I3
classify (False,False) = (0,0,0)
classify (False, True) = (1,0,0)
classify ( True,False) = (0,1,0)
classify ( True, True) = (0,0,1)

count :: String -> (I3, Int)
count (s0:s) = (classify (na, nb), n) where
    na = last s == 'A'
    nb = s0 == 'B'
    n = length [() | (c1, c2) <- zip (s0:s) s, c1 == 'A' && c2 == 'B']