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)

#![allow(unused, non_snake_case, dead_code, non_upper_case_globals)]
#![macro_use]

use std::cmp::*;
use std::collections::*;
use std::io::prelude::*;
use std::mem::*;
use std::num::*;
use std::slice::*;

const MOD: isize = 1_000_000_007;

fn main() {
    let N: usize = rd();
    // N以下の（A,B）の組
    // dp[i][10][10] // i 以下の数でAの末尾が{},Bの末尾が{}
    let mut cnt = vec![vec![0usize; 10]; 10];

    for i in 1..N + 1 {
        let (h, t) = hd(i);
        cnt[h][t] += 1;
    }

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

    println!("{}", ans);
}
fn hd(n: usize) -> (usize, usize) {
    let t = n % 10;
    let mut h = t;
    let mut nt = n;
    while nt > 0 {
        h = nt % 10;
        nt /= 10;
    }
    (h, t)
}
fn rd<T>() -> T
where
    T: std::str::FromStr,
{
    let stdin = std::io::stdin();
    let next: String = stdin
        .lock()
        .bytes()
        .map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    next.parse().ok().unwrap()
}