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)

# util functions

# debug
$debugFlag = ( ARGV[0] != nil )
p "==== DEBUG MODE ====" if $debugFlag

def pd(str)
  p str if $debugFlag
end

# input
lc = 0
aonly = 0
bonly = 0
abboth = 0
intab = 0
while l = $stdin.gets do
  if lc == 0
  else
    input = l.chomp
    intab += input.scan("AB").length
    if input[0..0] == "B"
      if input[-1..-1] == "A"
        abboth += 1
      else
        bonly += 1
      end
    elsif input[-1..-1] == "A"
      aonly += 1
    end
  end
  lc += 1
end

print "abboth:" if $debugFlag
pd abboth
print "aonly:" if $debugFlag
pd aonly
print "bonly:" if $debugFlag
pd bonly
print "intab:" if $debugFlag
pd intab

# body

min = [aonly, bonly].min
max = [aonly, bonly].max

delta = 0
if abboth - [(max - min), abboth].min > 0
  delta = (abboth - [(max - min), abboth].min)
  if max == min
    delta -= 1
  end
end

puts intab + min + [(max - min), abboth].min + delta