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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

#if DEBUG
using Microsoft.VisualStudio.TestTools.UnitTesting;
#endif

using System;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Threading.Tasks;

namespace Contest
{
    class Program
    {
        static long mod = 1000000007;

        static void Main(string[] args)
        {
            var scanner = new IO.StreamScanner(Console.OpenStandardInput());
            var n = scanner.Integer();
            var strs = new List<string>();
            for (int i = 0; i < n; i++) strs.Add(scanner.ScanLine());

            var ans = GetAns(n, strs);
            IO.Printer.Out.WriteLine(ans);
            IO.Printer.Out.Flush();
        }
        
        public static long GetAns(int n, List<string> strs)
        {
            var b_a = new Stack<string>();
            var x_a = new Stack<string>();
            var b_x = new Stack<string>();
            var other = new Stack<string>();

            foreach(var str in strs)
            {
                if (str[0] == 'B' && str.Last() == 'A') b_a.Push(str);
                else if (str[0] == 'B') b_x.Push(str);
                else if (str.Last() == 'A') x_a.Push(str);
                else other.Push(str);
            }

            if (b_a.Any())
            {
                // joint all b_a
                var str = new StringBuilder();
                while (b_a.Any()) str.Append(b_a.Pop());
                var abStr = str.ToString();

                // append b_x if possible
                if (b_x.Any()) abStr += b_x.Pop();

                // append to x_a if possible
                if (x_a.Any()) abStr = x_a.Pop() + abStr;

                other.Push(abStr);
            }

            // joint x_a and b_x
            while(x_a.Any() && b_x.Any())
            {
                other.Push(x_a.Pop() + b_x.Pop());
            }

            while (x_a.Any()) other.Push(x_a.Pop());
            while (b_x.Any()) other.Push(b_x.Pop());

            var ret = 0L;
            while (other.Any()) ret += Count(other.Pop());

            return ret;
        }

        public static long Count(string str)
        {
            var ret = 0L;
            if (str.Length < 2) return 0L;
            for(int i=0; i<str.Length - 1; i++)
            {
                if (str[i] == 'A' && str[i + 1] == 'B') ret++;
            }
            return ret;
        }
    }


#if DEBUG

    [TestClass]
    public class Test
    {
        [TestMethod]
        public void Test1()
        {

        }

        public bool IsEq<T> (List<T> l1, List<T> l2)
        {
            if (l1.Count() != l2.Count()) return false;
            for(int i=0; i<l1.Count(); i++)
            {
                if (!l1[i].Equals(l2[i])) return false;
            }
            return true;
        }
    }

#endif
}

namespace IO
{
    using System.IO;
    using System.Text;
    using System.Globalization;

    public class Printer : StreamWriter
    {
        static Printer()
        {
            Out = new Printer(Console.OpenStandardOutput()) { AutoFlush = false };
        }

        public static Printer Out { get; set; }

        public override IFormatProvider FormatProvider
        {
            get { return CultureInfo.InvariantCulture; }
        }

        public Printer(Stream stream)
            : base(stream, new UTF8Encoding(false, true))
        {
        }

        public Printer(Stream stream, Encoding encoding)
            : base(stream, encoding)
        {
        }

        public void Write<T>(string format, T[] source)
        {
            base.Write(format, source.OfType<object>().ToArray());
        }

        public void WriteLine<T>(string format, T[] source)
        {
            base.WriteLine(format, source.OfType<object>().ToArray());
        }
    }

    public class StreamScanner
    {
        public StreamScanner(Stream stream)
        {
            str = stream;
        }

        public readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof;

        public bool IsEndOfStream
        {
            get { return isEof; }
        }

        private byte read()
        {
            if (isEof) return 0;
            if (ptr < len) return buf[ptr++];
            ptr = 0;
            if ((len = str.Read(buf, 0, 1024)) > 0) return buf[ptr++];
            isEof = true;
            return 0;
        }

        public char Char()
        {
            byte b;
            do b = read(); while ((b < 33 || 126 < b) && !isEof);
            return (char)b;
        }

        public string Scan()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                sb.Append(b);
            return sb.ToString();
        }

        public string ScanLine()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b != '\n'; b = (char)read())
                if (b == 0) break;
                else if (b != '\r') sb.Append(b);
            return sb.ToString();
        }

        public long Long()
        {
            if (isEof) return long.MinValue;
            long ret = 0;
            byte b;
            var ng = false;
            do b = read(); while (b != 0 && b != '-' && (b < '0' || '9' < b));
            if (b == 0) return long.MinValue;
            if (b == '-')
            {
                ng = true;
                b = read();
            }
            for (; ; b = read())
            {
                if (b < '0' || '9' < b)
                    return ng ? -ret : ret;
                ret = ret * 10 + b - '0';
            }
        }

        public int Integer()
        {
            return (isEof) ? int.MinValue : (int)Long();
        }

        public double Double()
        {
            var s = Scan();
            return s != "" ? double.Parse(s, CultureInfo.InvariantCulture) : double.NaN;
        }

        static T[] enumerate<T>(int n, Func<T> f)
        {
            var a = new T[n];
            for (int i = 0; i < n; ++i) a[i] = f();
            return a;
        }

        public char[] Char(int n)
        {
            return enumerate(n, Char);
        }

        public string[] Scan(int n)
        {
            return enumerate(n, Scan);
        }

        public double[] Double(int n)
        {
            return enumerate(n, Double);
        }

        public int[] Integer(int n)
        {
            return enumerate(n, Integer);
        }

        public long[] Long(int n)
        {
            return enumerate(n, Long);
        }
    }
}