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_list = N.times.map { gets.chomp.chars }
count = s_list.map do |s|
  c = 0
  prev = nil
  s.each do |ch|
    if prev == 'A' && ch == 'B'
      c += 1
    end
    prev = ch
  end
  c
end.reduce(0) { |acc, n| acc + n }
a_count = s_list.count do |s|
  s[-1] == 'A'
end
b_count = s_list.count do |s|
  s[0] == 'B'
end
a_and_b_count = s_list.count do |s|
  s[0] == 'B' && s[-1] == 'A'
end
a_count -= a_and_b_count
b_count -= a_and_b_count
rest_count = begin
  c = 0
  while a_and_b_count > 0
    if a_count > 0 && b_count > 0
      c += 2
      a_count -= 1
      b_count -= 1
      a_and_b_count -= 1
    elsif a_count > 0
      c += 1
      a_count -= 1
      b_count += 1
      a_and_b_count -= 1
    elsif b_count > 0
      c += 1
      a_count += 1
      b_count -= 1
      a_and_b_count -= 1
    else
      c += a_and_b_count - 1
      a_and_b_count = 0
    end
  end
  c + [a_count, b_count].min
end
ans = count + rest_count
puts ans