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 OCaml (4.02.3) (judge verdict: Accepted)

let acc_ab n s =
  snd @@ Array.fold_left (fun (c, n) c' ->
    (c', n + if c = 'A' && c' = 'B' then 1 else 0)) ('_', n) @@
  Array.init (String.length s) (String.get s)

let () = Scanf.scanf "%d\n" @@ fun n ->
  let ss = Array.init n @@ fun _ -> Scanf.scanf "%s\n" @@ fun s -> s in
  let (a, b, ba) =
    Array.fold_left (fun (a, b, ba) s ->
      if s.[0] = 'B' && s.[String.length s - 1] = 'A' then (a, b, ba + 1)
      else if s.[0] = 'B' then (a, b + 1, ba)
      else if s.[String.length s - 1] = 'A' then (a + 1, b, ba)
      else (a, b, ba)) (0, 0, 0) ss in
  let n = min a @@ min b ba in
  Printf.printf "%d\n" @@
  Array.fold_left acc_ab 0 ss +
  if a <= 0 && b <= 0 then max 0 (ba - 1) else ba + min a b