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)

#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::*;

use std::io::*;
use std::str::FromStr;

fn read<T: FromStr>() -> T {
  let stdin = stdin();
  let stdin = stdin.lock();
  let token: String = stdin
    .bytes()
    .map(|c| c.expect("failed reading char") as char)
    .skip_while(|c| c.is_whitespace())
    .take_while(|c| !c.is_whitespace())
    .collect();
  token.parse().ok().expect("failed parsing")
}

fn pair(x: usize) -> (usize, usize) {
  let a: usize = x % 10;
  let b: usize = x
    .to_string()
    .chars()
    .nth(0)
    .unwrap()
    .to_string()
    .parse::<usize>()
    .unwrap();
  (a, b)
}

fn main() {
  let n: usize = read::<usize>();

  let mut freq: HashMap<(usize, usize), usize> = HashMap::new();

  for i in 1..(n + 1) {
    let p = pair(i);
    freq.entry(p).or_insert(0);
    let count = freq.get(&p).unwrap() + 1;
    freq.insert(p, count);
  }

  let mut ans: usize = 0;

  for i in 1..(n + 1) {
    let p = pair(i);
    let q = (p.1, p.0);
    match freq.get(&q) {
      Some(n) => {
        ans = ans + n;
      }
      None => {}
    }
  }

  println!("{}", ans);
}