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.Monad
import Data.List
f s n
 |null s=n
 |null (init s)=n
 |s!!0=='A'&&s!!1=='B'=f(drop 1 s)(n+1)
 |otherwise=f(drop 1 s)n
ga x=if take 2 x=="AB" then True else False
gb x=if last x=='B'&&last(init x)=='A' then True else False
main=do
 n<-readLn :: IO Int
 ss<-replicateM n getLine
 let sr=sum$map(\x->f(tail (init x))0)ss
     sa=sum$map(\x->if head x=='B' then 1 else 0)ss
     sb=sum$map(\x->if last x=='A' then 1 else 0)ss
     sp=max (min(sa-1)sb) (min(sb-1)sa)
     sq=if sb<=0 then 0 else sp
     pa=sum$map(\x->if ga x then 1 else 0)ss
     pb=sum$map(\x->if gb x then 1 else 0)ss
     pq=sum$map(\x->if ga x&&gb x then 1 else 0)ss
     pp=if pa==1&&pb==1&&pq==1 then 1 else (\x->if x>=1 then 1 else 0)pa+(\x->if x>=1 then 1 else 0)pb
     
 print$sr+sq+pp