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 9.2.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <string>
#include <vector>
#include <algorithm>
#include <numeric>
#include <map>
#include <stack>
#include <queue>
#include <iomanip>
#include <set>
using namespace std;
using ll = long long;
using P = pair<ll, ll>;

int main()
{
    int n;
    cin >> n;
    vector<string> s(n);
    for (int i = 0; i < n; ++i) cin >> s[i]; 
    ll ab = 0, lb = 0, ra = 0;
    ll ans = 0;
    for (int i = 0; i < n; ++i)
    {
        if (s[i][0] == 'B' && s[i][s[i].size() - 1] == 'A') ++ab;
        else if (s[i][0] == 'B') ++lb;
        else if (s[i][s[i].size() - 1] == 'A') ++ra;
        for (int k = 0; k < s[i].size() - 1; ++k)
        {
            if (s[i][k] == 'A' && s[i][k + 1] == 'B')
                ++ans;
        }
    }
    ll d = abs(lb - ra);
    ll add;
    if (ab - d >= 0)
    {
        add = max(ra, lb) + ab - d;
    }
    else
    {
        add = min(lb, ra);
        if (ab - d > 1)
        {
            add += ab + 1;
        }
        else
        {
            add += ab;
        }
        
    }
    ans += add;
    cout << ans << endl; 
    return 0;
}