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 Ruby (2.3.3) (judge verdict: Wrong Answer)

N = gets.to_i
S = N.times.map { gets.chomp }

ans = 0

S.each do |s|
  l = s.size

  0.upto(l - 2) do |i|
    ans += 1 if s[i..(i + 1)] == 'AB'
  end
end

acnt = S.count { |s| s[-1] == 'A' && s[0] != 'B' }
bcnt = S.count { |s| s[0] == 'B' && s[-1] != 'A' }
ccnt = S.count { |s| s[0] == 'B' && s[-1] == 'A' }

rcnt = [acnt, bcnt].min
ans += rcnt

acnt -= rcnt
bcnt -= rcnt

ncnt = [acnt, ccnt].min
ans += ncnt
ccnt -= ncnt

mcnt = [bcnt, ccnt].min
ans += mcnt
ccnt -= mcnt

if ncnt > 0 || mcnt > 0
  ans += ccnt
else
  ans += [0, ccnt - 1].max
end

puts ans