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)

use proconio::input;
use std::collections::HashMap;

fn helper(mut n: usize) -> (usize, usize) {
  let a = n % 10;
  let mut b = 0;
  while 0 < n {
    b = n;
    n /= 10;
  }
  (a, b)
}

fn main() {
  input! {
    n: usize,
  }

  let mut map: HashMap<(usize, usize), usize> = HashMap::new();
  for i in 1..=n {
    let p = helper(i);
    let mut entry = map.entry(p).or_insert(0);
    *entry += 1;
  }

  let mut count = 0;
  for i in 1..=n {
    let (a, b) = helper(i);
    count += map.get(&(b,a)).unwrap_or(&0);
  }

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