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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<iostream>
#include<algorithm>
#include<string>
#include<cstdlib>
#include<map>
#include<iomanip>
#include<sstream>
#include<vector>
#include<stack>
#include<math.h>

using namespace std;
string str[10005];

int main()
{
	
	long long int n, m, a[2000000],r,g,b,res=0,a_fin=0,b_start=0,a_fin_b_start=0;
	cin >>n;
	for (int i = 0; i < n; i++) {
		cin >> str[i];
		for (int j = 0; j < str[i].length() - 1; j++) {
			if (str[i].substr(j, 2) == "AB") {
				res++;
			}
		}
		if (str[i][0] == 'B' && str[i][str[i].length() - 1] == 'A') {
			a_fin_b_start++;
		}
		else if (str[i][0] == 'B') {
			b_start++;
		}
		else if (str[i][str[i].length() - 1] == 'A') {
			a_fin++;
		}
	}
	if (a_fin_b_start == 0) {
		cout<< res+min(a_fin, b_start);
		return 0;
	}
	if (a_fin > 0&&b_start>0) {
		a_fin--;
		b_start--;
		res += a_fin_b_start+1;
		res += min(a_fin, b_start);
	}
	else if(a_fin > 0 || b_start > 0) {
		res += a_fin_b_start;
	}
	else {
		res+= a_fin_b_start-1;
	}
	cout << res;
}