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 (1.15.1) (judge verdict: Accepted)

use std::io::Read;

fn main() {
    let mut s: String = String::new();
    std::io::stdin().read_to_string(&mut s).ok();
    let n: usize = s.trim().parse().unwrap();
    let mut mp = std::collections::HashMap::<(u8, u8), u64>::new();
    let mut ans = 0u64;
    for i in 1..n + 1 {
        let s: Vec<u8> = i
            .to_string()
            .chars()
            .map(|c| c.to_digit(10).unwrap() as u8)
            .collect();
        let cnt = mp.entry((s[0], s[s.len() - 1])).or_insert(0);
        *cnt += 1;
    }
    for i in 1..10 {
        for j in 1..10 {
            match (mp.get(&(i, j)), mp.get(&(j, i))) {
                (Some(val1), Some(val2)) => ans += val1 * val2,
                _ => (),
            }
        }
    }
    println!("{}", ans);
}