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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
#define max(a,b) ((a)>(b)?(a):(b))
#define min(a,b) ((a)<(b)?(a):(b))

int main(){
	int n,i,j;
	char s[10000][11];
	scanf("%d",&n);
	for(i=0;i<n;i++)scanf("%s",s[i]);
	int ans=0,ge[1000],ha=0,ow=0,hajio=0;
	for(i=0;i<n;i++){
		for(j=0;s[i][j+1]!=0;j++){
			if(s[i][j]=='A'&&s[i][j+1]=='B')ans++;
		}
		ge[i]=j;
	}
	for(i=0;i<n;i++){
		if(s[i][0]=='B'&&s[i][ge[i]]=='A')hajio++;
		else if(s[i][0]=='B')ha++;
		else if(s[i][ge[i]]=='A')ow++;
	}
	if(hajio<max(ha,ow)-min(ha,ow)){
		ans+=min(ha,ow)+hajio;
	}else{
		ans+=max(ha,ow);
		hajio-=max(ha,ow)-min(ha,ow);
		ans+=hajio/2;
	}
	printf("%d\n",ans);
	return 0;
}