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: Runtime Error)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use competitive::prelude::*;

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

    s.sort_by_key(|r| r.len());

    let mut mm = BTreeMap::<(&[char], char), usize>::new();
    let mut ans = 0;

    for r in s.iter() {
        let mut b = 0_u64;
        for i in 0..r.len() {
            b |= 1 << ((r[i] as u8 - b'a') as usize);
            let rr = &r[i + 1..];

            use std::ops::Bound::*;
            for t in mm.range((Included((rr, 'a')), Included((rr, 'z')))) {
                let c = t.0 .1;
                if b & (1 << ((c as u8 - b'a') as usize)) != 0 {
                    ans += t.1;
                }
            }
        }

        *mm.entry((&r[1..], r[0])).or_default() += 1;
    }

    echo!(ans);
}
*/

fn main() {
    let exe = "/tmp/binE623C421";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "
0VMRgIBAQAAAAAAAAAAAAIAPgABAAAAuA5CAAAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAEAAOAADAEAA
AAAAAAEAAAAFAAAAAAAAAAAAAAAAAEAAAAAAAAAAQAAAAAAAuBYCAAAAAAC4FgIAAAAAAAAAIAAAAAAA
AQAAAAYAAABIDQAAAAAAAEidZAAAAAAASJ1kAAAAAAAAAAAAAAAAAAAAABAAAAAAAABR5XRk
BgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAQAAAAAAAAAPytLH5VUFgh
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