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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#define mp make_pair
#define pb push_back
#define re return
typedef long long ll;
typedef pair<int, int> pii;
int n;
string s[10100];
pair<bool,bool> a[10010];
ll ans;
int tp1,tp2,tp3;
int main() { 
    //freopen("input.txt","r",stdin);
	//freopen("output.txt","w",stdout);
	cin>>n;
	for(int i=0;i<n;i++){
		cin>>s[i];
		for(int j=1;j<s[i].size();j++){
			if(s[i][j]=='B' && s[i][j-1]=='A')ans++;
		}
		
		if(s[i][0]=='B')a[i].first=1;
		if(s[i][s[i].size()-1]=='A')a[i].second=1;
		
		if(a[i].first && a[i].second)tp2++;
		else{
			if(a[i].first)tp3++;
			if(a[i].second)tp1++;
		}
	}
	ans+=tp2+1;
	tp3--;
	tp1--;
	if(tp3==-1){
		ans--;
		tp3=0;
	}
	if(tp1==-1){
		ans--;
		tp1=0;
	}
	ans+=min(tp3,tp1);
	if(tp2==0)ans++;
	cout<<ans<<endl;
    return 0; 
}