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<cstring>
using namespace std;
const int maxn=1e6;
string s[maxn];
int main(){
	int n,A=0,B=0,AB=0,sum=0;
	cin>>n;
	for(int i=0;i<n;i++){
		cin>>s[i];
		int len=s[i].size()-1;
		for(int j=1;j<=len;j++){
			if(s[i][j]=='B'&&s[i][j-1]=='A') sum++;
		}
		if(s[i][0]=='B'&&s[i][len]=='A'){
			AB++;continue;
		}
		if(s[i][0]=='B'){
			B++;continue;
		}
		if(s[i][len]=='A'){
			A++;continue;
		}
	}
	int ans=0;
	if(AB>0){
		if(A>0||B>0){
			A--; B--;
			ans+=2;AB--;			
		}
		else AB--;
	}
	ans+=min(A,B)+AB+sum;
	cout<<ans<<endl;
	return 0;
}