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 Scala (2.11.7) (judge verdict: Accepted)

import java.io.{BufferedReader, InputStreamReader}

import scala.collection.mutable

object Main {
  def main(args: Array[String]): Unit = {
    val in = new BufferedReader(new InputStreamReader(System.in))
    val n = in.readLine().toInt

    val memo = new mutable.HashMap[(Char, Char), Int]()

    for {
      i <- 1 to n
    } {
      val s = i.toString
      val head = s.head
      val last = s.last

      if (last != '0') {
        val key = (head, last)
        memo.update(key, memo.getOrElseUpdate(key, 0) + 1)
      }
    }

    var count = 0
    for {
      i <- '1' to '9'
      j <- '1' to '9'
    } {
      count += memo.getOrElse((i, j), 0) * memo.getOrElse((j, i), 0)
    }

    System.out.println(count)
  }
}