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 <iostream>
#include <algorithm>
#include <vector>
#include <string>
#define REP(i, n) for (int i = 0; i < (n); i++)
#define ALL(a) a.begin(), a.end()

using namespace std;

int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  int N;
  cin >> N;
  vector<vector<string>> T(4);
  REP(i, N) {
    string S;
    cin >> S;
    if (S.front() == 'B' && S.back() == 'A') {
      T[2].push_back(S);
    } else if (S.back() == 'A') {
      T[0].push_back(S);
    } else if (S.front() == 'B') {
      T[1].push_back(S);
    } else {
      T[3].push_back(S);
    }
  }
  string s;
  while (T[0].size() > 0 && T[1].size() > 0) {
    s += T[0].back(); T[0].pop_back();
    s += T[1].back(); T[1].pop_back();
  }
  if (T[0].size() > 0) {
    s += T[0].back(); T[0].pop_back();
  }
  while (T[2].size() > 0) {
    s += T[2].back(); T[2].pop_back();
  }
  if (T[1].size() > 0) {
    s += T[1].back(); T[1].pop_back();
  }
  for (int i = 0; i < 4; i++) {
    while (T[i].size() > 0) {
      s += T[i].back(); T[i].pop_back();
    }
  }
  int ans = 0;
  REP(i, s.size() - 1) {
    if (s[i] == 'A' && s[i+1] == 'B') ans++;
  }
  cout << ans << '\n';
}