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)

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn get_first(i: u32) -> u32 {
    i.to_string().chars().nth(0).unwrap().to_digit(10).unwrap()
}

fn get_last(i: u32) -> u32 {
    i % 10
}

fn count(first: u32, last: u32, n: u32) -> u32 {
    let mut count = 0;

    // 1桁の場合
    if first == last && first <= n {
        count += 1;
    }

    // 2桁の場合
    if 10 * first + last <= n {
        count += 1;
    }

    // 3桁以上の場合
    let mut d = 1;
    loop {
        let mut m = first * 10u32.pow(d + 1) + last;
        for x in 1..d + 1 {
            m += 9 * 10u32.pow(x);
        }

        if m > n {
            let x = first * 10u32.pow(d + 1) + last;
            if x < n {
                count += (n - x) / 10 + 1;
            }
            break;
        }

        count += 10u32.pow(d);
        d += 1;
    }

    count
}

fn main() {
    let n: u32 = read();

    let mut ans = 0;
    for a in 1..n + 1 {
        let first = get_first(a);
        let last = get_last(a);
        if last == 0 {
            continue;
        }
        ans += count(last, first, n);
    }

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