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)

{-# LANGUAGE BangPatterns #-}
import Control.Monad
import Data.Maybe
import Debug.Trace
import Data.List
import qualified Data.Map.Strict as Map
import qualified Data.IntMap.Strict as IntMap
import qualified Data.Set as Set
import qualified Data.IntSet as IntSet
import Data.Functor
import Data.Array
-- import Data.Array.Unboxed
import Control.Monad.ST
import Data.Array.ST

main :: IO ()
main = do
  n <- readLn :: IO Int
  ss <- replicateM n getLine :: IO [String]
  print $ solve ss

solve :: [String] -> Int
solve ss = (min endWithA startWithB) + orgAb
  where
    endWithA = sum $ map countA ss
    startWithB = sum $ map countB ss
    
    orgAb = sum $ map countAb ss

countAb (s:[]) = 0
countAb (s1:s2:s3) = (if s1 == 'A' && s2 == 'B' then 1 else 0) + countAb (s2:s3)

countA s = if last s == 'A' then 1 else 0
countB s = if head s == 'B' then 1 else 0