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)

##templete
n = gets.chomp.to_i
strings = []
n.times do
  strings.push(gets.chomp)
end

innerAB = 0

for str in strings do
  index = 0
  while index < str.length - 1 do
    if str[index] == 'A'
      if str[index + 1] == 'B'
        innerAB += 1
        index += 2
      end
    end
    index += 1
  end
end


headB = 0
tailA = 0
sameAB = 0

for str in strings do
  if str[0] == "B" && str[-1] == "A"
    sameAB += 1
  elsif str[0] == "B"
    headB += 1
  elsif str[-1] == "A"
    tailA += 1
  end
end

ans = [sameAB - 1, 0].max
sameAB = 1

if headB > tailA
  ans += tailA
  headB -= tailA
  ans += [headB, sameAB].min
else
  ans += headB
  tailA -= headB
  ans += [tailA, sameAB].min
end

puts ans + innerAB