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
import Data.List
f n s
 |null s=n
 |null (init s)=n
 |s!!0=='A'&&s!!1=='B'=f(n+1)(drop 1 s)
 |otherwise=f(n)(drop 1 s)
main=do
 n<-readLn :: IO Int
 ss<-replicateM n getLine
 let sr=sum$map(f 0)ss
     sa=sum$map(\x->if head x=='B' &&last x/='A'then 1 else 0)ss
     sb=sum$map(\x->if last x=='A' &&head x/='B'then 1 else 0)ss
     ab=sum$map(\x->if head x=='B' &&last x=='A'then 1 else 0)ss
     sq=if sa==0&&sb==0&&ab==0 then sa+sb else if sa==0&&sb==0 then ab-1 else if sa==0||sb==0 then ab else ab+1+(min (sa-1) (sb-1))
 print$sr+sq