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)

// -*- coding:utf-8-unix -*-

// use proconio::derive_readable;
use proconio::fastout;
use proconio::input;
// use std::convert::TryInto;
use libm::*;
use std::cmp::*;
use std::io::*;
use std::str::FromStr;
use superslice::*;

pub fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

//abc152-D
#[fastout]
fn main() {
    input![n: u64];

    let mut comb = vec![0; 100];

    for i in 1..(n + 1) {
        if i % 10 == 0 {
            continue;
        }

        let d1 = i % 10;
        let mut d10 = i;
        while d10 > 9 {
            d10 /= 10;
        }

        let key = (d1 + d10 * 10) as usize;
        // eprintln!("i:{}, key; {}", i, key);
        comb[key] += 1;
    }

    let mut ans = 0;

    // let mut idx = 1;
    let mut is_visits = vec![false; 100];
    for (idx, c) in comb.iter().enumerate() {
        if is_visits[idx as usize] {
            continue;
        }

        if *c > 0 {
            // eprintln!(
            //     "idx + 1: {}, comb: {}, +{}",
            //     idx + 1,
            //     c,
            //     max(0, (c * (c - 1) / 2) + c as u64)
            // );

            let d1 = (idx) % 10;
            let mut d10 = idx;
            while d10 > 9 {
                d10 /= 10;
            }
            let inv_idx = (d1 * 10 + d10 * 1) as usize;

            ans += comb[inv_idx as usize] * c;
            // eprintln!(
            //     "idx: {}, inv_idx: {}, c: {}, c_inv: {}",
            //     idx, inv_idx, c, comb[inv_idx as usize]
            // );

            // is_visits[idx] = true;
            // is_visits[inv_idx] = true;
        }
    }

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