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

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

    let mut c: Vec<Vec<usize>> = vec![];
    for i in 0..10 {
        c.push(vec![]);
        for j in 0..10 {
            c[i].push(0);
            for x in 1..n+1 {
                let (a, b) = f(x);
                if a == i && b == j {
                    c[i][j] += 1;
                }
            }
        }
    }
    let mut ans = 0;
    for i in 0..10 {
        for j in 0..10 {
            ans += c[i][j] * c[j][i];
        }
    }
    println!("{}", ans);
}