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
a = Array.new
b = Array.new
ab = Array.new
ans = 0

n.times do
  s = gets.chomp.gsub(/AB/, '!')
  ans += s.count('!')
  if s[0] == 'B' and s[-1] == 'A'
    ab << s
  elsif s[0] == 'B'
    b << s
  elsif s[-1] == 'A'
    a << s
  end
end

as = a.size
bs = b.size
abs = ab.size

if as == 0 and bs == 0
  if abs == 0
    puts ans
  else
    ans += abs / 2
    puts ans
  end
elsif as == 0 or bs == 0
  if abs == 0
    puts ans
  else
    if as == 0
      if abs <= bs
        ans += abs
        puts ans
      else
        ans += bs
        ans += abs - bs
        puts ans
      end
    else
      if abs <= as
        ans += abs
        puts ans
      else
        ans += as
        ans += abs - as
        puts ans
      end
    end
  end
else
  if abs == 0
    if as <= bs
      ans += as
    else
      ans += bs
    end
    puts ans
  else
    if as == bs
      ans += as
      ans += abs / 2
    elsif as < bs
      ans += as
      t = bs - as
      if t == abs
        ans += t
      elsif t < abs
        ans += t
        ans += abs - t
      else
        ans += abs
      end
    elsif as > bs
      ans += bs
      t = as - bs
      if t == abs
        ans += t
      elsif t < abs
        ans += t
        ans += abs - t
      else
        ans += abs
      end
    end
    puts ans
  end
end