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>
#include <assert.h>
using namespace std;
using i64 = long long;

int main()
{
  i64 n;
  cin >> n;
  vector<string> s(n);
  for (i64 i = 0; i < n; i++)
    cin >> s[i];
  i64 ans = 0, ea = 0, sb = 0, ab = 0;
  for (i64 i = 0; i < n; i++)
  {
    if (s[i][0] == 'A' && s[i][s[i].size() - 1] == 'B')
      ab++;
    else if (s[i][s[i].size() - 1] == 'A')
      ea++;
    if (s[i][0] == 'B')
      sb++;
    for (i64 j = 0; j < s[i].size() - 1; j++)
      if (s[i].substr(j, 2) == "AB")
        ans++;
  }
  cout << ans + min(ea, sb) + min(abs(ea - sb), ab) + (0 < ab - abs(ea - sb) ? ab - abs(ea - sb) / 2 : 0) << endl;
  return 0;
}