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 Scala (2.11.7) (judge verdict: Accepted)

import scala.io.{StdIn => in}

object Main extends App {
  val n = in.readInt
  val sn = Iterator.continually(in.readLine).take(n).toArray

  val tar = "AB"
  var sum1 = sn.map(_.sliding(2).count(_ == tar)).sum

  val (b_, _a, ba) = sn./:(0,0,0) {
    case ((x, y, z), s) if s.head == 'B' && s.last == 'A' => (x, y, z+1)
    case ((x, y, z), s) if s.head == 'B' => (x+1, y, z)
    case ((x, y, z), s) if s.last == 'A' => (x, y+1, z)
    case ((x, y, z), s) => (x, y, z)
  }

  val sum2 = ba match {
    case x if x == 0 => _a min b_
    case x if _a + b_ == 0 => ba - 1
    case _ => ba + (_a min b_)
  }
  // debug(sum1, ba, b_, _a)

  val ans = sum1 + sum2
  println(ans)

  def debug(any:Any*):Unit = {
    if(this.getClass.toString != "class Main$")
      println(any.mkString(" "))
  }
}