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)

#![allow(unused_imports)]

use proconio::{input, fastout};
use proconio::marker::*;
use std::cmp::{max, min};
use im_rc::HashMap;

#[fastout]
fn main() {
    input! {
    n: usize,
    }
    let mut map = vec![vec![0; 10]; 10];
    for i in 1..=n {
        let (t, b) = tb(i);
        map[t][b] += 1;
    }
    let mut ans = 0;
    for i in 1..=n {
        let (t, b) = tb(i);
        ans += map[b][t];
    }
    println!("{}", ans);
}


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