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: Accepted)

N = gets.to_i
s = Array.new(N)
for i in 0..(N-1)
  s[i] = gets.chomp.split("")
end
ab = Array.new(N).map{Array.new(3, 0)}
nAB = nBA = nA = nB = 0

for i in 0..(N-1)
  for j in 0..(s[i].size - 1)
    if j == 0 && s[i][j] == "B"
      ab[i][2] = 1
    elsif j == s[i].size - 1 && s[i][j] == "A"
      ab[i][1] = 1
    end
    if j < s[i].size - 1
      if s[i][j..(j+1)].join == "AB"
        ab[i][0] += 1
      end
    end
  end
  nAB += ab[i][0]
  if ab[i][1] == 1 && ab[i][2] == 1
    nBA += 1
  elsif ab[i][1] == 1
    nA += 1
  elsif ab[i][2] == 1
    nB += 1
  end
end

if nBA == 0
  puts nAB + [nA, nB].min
else
  if nA == 0 && nB == 0
    puts nAB + nBA - 1
  elsif nA == 0 || nB == 0
    puts nAB + nBA
  else
    puts nAB + nBA + 1 + [nA, nB].min - 1
  end
end