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: Accepted)

use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;
#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
#[allow(unused_imports)]
use std::f64::consts::*;

#[allow(unused)]
const INF: usize = std::usize::MAX / 4;
#[allow(unused)]
const M: usize = 1000000007;

fn main() {
    input! {
        n: usize,
        mut s: [Chars; n],
    }
    for i in 0..n {
        s[i].reverse();
    }
    s.sort();
    // for i in 0..n {
    //     eprintln!("{} {:?}", i, s[i]);
    // }
    let mut last_index = vec![vec![-1; 26]; n];
    for i in 0..n {
        for (j, &c) in s[i].iter().enumerate() {
            let c = c as usize - 'a' as usize;
            last_index[i][c] = j as isize;
        }
    }
    // for i in 0..n {
    //     eprintln!("{:?}", last_index[i]);
    // }

    let mut prefix = vec![0; n];
    for i in 1..n {
        let mut k = 0;
        while k < s[i - 1].len() - 1 && k < s[i].len() - 1 && s[i - 1][k] == s[i][k] {
            k += 1;
        }
        prefix[i] = k;
    }
    // eprintln!("{:?}", prefix);

    // let mut debug = 0;
    // for i in 0..n {
    //     for j in 0..n {
    //         if s[i].len() >= s[j].len() {
    //             continue;
    //         }
    //         let l = s[i].len() - 1;
    //         if (0..l).all(|k| s[i][k] == s[j][k]) && (l..s[j].len()).any(|k| s[j][k] == s[i][l]) {
    //             eprintln!("{} {}", i, j);
    //             debug += 1;
    //         }
    //     }
    // }
    // eprintln!("{}", debug);

    let mut result = 0usize;
    for i in 0..n - 1 {
        let length = prefix[i + 1];
        if s[i].len() - 1 != length {
            continue;
        }
        let c = s[i][length] as usize - 'a' as usize;
        for j in i + 1..n {
            if prefix[j] < length {
                break;
            }
            if last_index[j][c] >= length as isize {
                // eprintln!("{} {}", i, j);
                result += 1;
            }
        }
    }
    // for i in 0..n {
    //     if s[i].len() == 1 {
    //         let c = s[i][0] as usize - 'a' as usize;
    //         for j in 0..i {
    //             if last_index[j][c] >= 0 {
    //                 eprintln!("{} {}", i, j);
    //                 result += 1;
    //             }
    //         }
    //     }
    // }
    //
    //
    s.reverse();
    last_index.reverse();
    let mut prefix = vec![0; n];
    for i in 1..n {
        let mut k = 0;
        while k < s[i - 1].len() - 1 && k < s[i].len() - 1 && s[i - 1][k] == s[i][k] {
            k += 1;
        }
        prefix[i] = k;
    }
    for i in 0..n - 1 {
        let length = prefix[i + 1];
        if s[i].len() - 1 != length {
            continue;
        }
        let c = s[i][length] as usize - 'a' as usize;
        for j in i + 1..n {
            if prefix[j] < length {
                break;
            }
            if last_index[j][c] >= length as isize {
                // eprintln!("{} {}", i, j);
                result += 1;
            }
        }
    }
    println!("{}", result);
}