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 Rust (1.42.0) (judge verdict: Wrong Answer)

#![allow(unused, non_snake_case, dead_code, non_upper_case_globals)]
use {
    proconio::{marker::*, *},
    std::{cmp::*, collections::*, mem::*},
};

fn main() {
    input! {
        n:usize,
        s:[Chars;n],
    }

    let mut ans = 0;
    let mut st = 0;
    let mut ed = 0;
    let mut both = 0;
    for c in s.clone() {
        let n = c.len();
        if c[0] == 'B' && c[n - 1] == 'A' {
            both += 1;
        } else {
            if c[0] == 'B' {
                st += 1;
            }
            if c[n - 1] == 'A' {
                ed += 1;
            }
        }
        for i in 0..n - 1 {
            if c[i] == 'A' && c[i + 1] == 'B' {
                ans += 1;
            }
        }
    }
    // ed -> both -> both ... -> ed -> st -> ed -> st -> any()

    // ed -> st -> ed -> st -> ed -> st -> both -> both -> ...
    st += both;
    ed += both;

    if st == 0 && ed == 0 && both != 0 {
        ans += both - 1;
    } else {
        ans += min(n - 1, min(st, ed));
    }
    println!("{}", ans);
}