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::{self, BufRead};

fn main() {
    let stdin = io::stdin();
    let mut lines = stdin.lock().lines();
    let n: i32 = lines.next().unwrap().unwrap().parse().unwrap();

    let mut digit: Vec<Vec<i64>> = vec![vec![0; 10]; 10];
    for i in 1..n + 1 {
        let begin: usize = i.to_string().chars().next().unwrap().to_digit(10).unwrap() as usize;
        let end: usize = (i % 10) as usize;
        if end == 0 {
            continue;
        }
        digit[begin][end] += 1;
    }

    let mut ans = 0;
    for i in 1..10 {
        for j in 1..10 {
            ans += digit[i][j] * digit[j][i];
        }
    }

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