Problem:
Score : 400 points

Problem Statement

Given is a positive integer N.

Find the number of pairs (A, B) of positive integers not greater than N that satisfy the following condition:

When A and B are written in base ten without leading zeros, the last digit of A is equal to the first digit of B, and the first digit of A is equal to the last digit of B.

Constraints

1 \leq N \leq 2 \times 10^5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N

Output

Print the answer.

Sample Input 1

25

Sample Output 1

17

The following 17 pairs satisfy the condition: (1,1), (1,11), (2,2), (2,22), (3,3), (4,4), (5,5), (6,6), (7,7), (8,8), (9,9), (11,1), (11,11), (12,21), (21,12), (22,2), and (22,22).

Sample Input 2

1

Sample Output 2

1

Sample Input 3

100

Sample Output 3

108

Sample Input 4

2020

Sample Output 4

40812

Sample Input 5

200000

Sample Output 5

400000008

Solution in Rust (1.42.0) (judge verdict: Accepted)

#[allow(unused_imports)]
use itertools::Itertools;
#[allow(unused_imports)]
use num::*;
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;
#[allow(unused_imports)]
use std::collections::*;

fn solve() {
    input! {
        n: usize
    };

    let mut ht_counts = HashMap::new();
    for x in 1..=n {
        let chars = x
            .to_string()
            .chars()
            .map(|ch| ch.to_digit(10).unwrap() as usize)
            .collect::<Vec<_>>();
        let head = chars[0];
        let tail = chars[chars.len() - 1];
        *ht_counts.entry((head, tail)).or_insert(0) += 1;
    }
    let mut res = 0_usize;
    for h in 1..=9 {
        for t in 1..=9 {
            match (ht_counts.get(&(h, t)), ht_counts.get(&(t, h))) {
                (Some(&a), Some(&b)) => {
                    res += a * b;
                }
                _ => {}
            }
        }
    }
    println!("{}", res);
}

fn main() {
    std::thread::Builder::new()
        .name("big stack size".into())
        .stack_size(256 * 1024 * 1024)
        .spawn(|| {
            solve();
        })
        .unwrap()
        .join()
        .unwrap();
}