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 <bits/stdc++.h>
#define MOD 1000000007LL
using namespace std;
typedef long long ll;
typedef pair<int,int> P;

int n;
string s[10005];
int type[10005];
int cnt[4];
int ans=0;

int main(void){
	scanf("%d",&n);
	for(int i=0;i<n;i++){
		cin >> s[i];
		if(s[i][0]=='B')type[i]+=1;
		if(s[i][s[i].size()-1]=='A')type[i]+=2;
		cnt[type[i]]++;
		int pr=0;
		for(int j=0;j<s[i].size();j++){
			if(s[i][j]=='A'){
				pr=1;
			}else if(s[i][j]=='B'){
				if(pr==1){
					ans++;
				}
				pr=0;
			}else{
				pr=0;
			}
		}
	}
	if(cnt[3]>=1){
		ans+=cnt[3]-1;
		if(cnt[1]>=1){
			cnt[1]--;
			ans++;
		}
		if(cnt[2]>=1){
			cnt[2]--;
			ans++;
		}
	}
	ans+=min(cnt[1],cnt[2]);
	printf("%d\n",ans);
	return 0;
}