Problem:
Score : 700 points

Problem Statement

Limak can repeatedly remove one of the first two characters of a string,
for example abcxyx \rightarrow acxyx \rightarrow cxyx \rightarrow cyx.

You are given N different strings S_1, S_2, \ldots, S_N.
Among N \cdot (N-1) / 2 pairs (S_i, S_j),
in how many pairs could Limak obtain one string from the other?

Constraints

2 \leq N \leq 200\,000

S_i consists of lowercase English letters a-z.

S_i \neq S_j

1 \leq |S_i|

|S_1| + |S_2| + \ldots + |S_N| \leq 10^6

Input

Input is given from Standard Input in the following format.

N
S_1
S_2
\vdots
S_N

Output

Print the number of unordered pairs (S_i, S_j)
where i \neq j and Limak can obtain one string from the other.

Sample Input 1

3
abcxyx
cyx
abc

Sample Output 1

1

The only good pair is (abcxyx, cyx).

Sample Input 2

6
b
a
abc
c
d
ab

Sample Output 2

5

There are five good pairs: (b, abc), (a, abc), (abc, c), (b, ab), (a, ab).

Solution in Rust (1.42.0) (judge verdict: Time Limit Exceeded)

#![allow(unused_imports)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

fn main() {
    let n = read::<usize>();
    let mut s = vec![];
    for i in 0..n {
        let mut ss = read::<String>()
            .chars()
            .map(|x| x.to_digit(36).unwrap() as usize - 10)
            .collect::<Vec<_>>();
        ss.reverse();
        s.push(ss);
    }

    s.sort_by_key(|x| x.len());
    // debug!(s);

    let mut count: HashMap<usize, HashMap<Vec<usize>, i64>> = HashMap::new();
    let mut ans = 0i64;
    for ss in s {
        let mut cur_key = vec![];
        let mut char_count = vec![0; 26];

        for &ch in &ss {
            char_count[ch] += 1;
        }

        for l in 1..ss.len() + 1 {
            if count.contains_key(&l) {
                for ai in 0..26 {
                    if char_count[ai] == 0 {
                        continue;
                    }
                    cur_key.push(ai);
                    if count[&l].contains_key(&cur_key) {
                        ans += count[&l][&cur_key];
                        // debug!(ss, cur_key);
                    }
                    cur_key.pop();
                }
            }
            cur_key.push(ss[l - 1]);
            char_count[ss[l - 1]] -= 1;
        }
        let mut y = count.entry(ss.len()).or_insert(HashMap::new());
        *y.entry(ss).or_insert(0) += 1;
    }
    // debug!(count);
    println!("{}", ans);
}

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}