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 Kotlin (1.0.0) (judge verdict: Wrong Answer)


fun main(args: Array<String>) {
    val n = readLine()!!.toInt()

    var ketasu = n.toString().length - 2
    val top = n.toString().first().toString().toInt()
    val bottom = n % 10

    var p1 = 0
    var p2 = 0
    var p3 = 0
    if (ketasu >= 1) {
        p1 = Math.pow(10.0, ketasu.toDouble()).toInt()
        p2 = Math.pow(10.0, ketasu - 1.0).toInt()
        p3 = n.toString().substring(1, ketasu + 1).toInt() 
    }
    if (p2 == 1) { p2 = 0 }

    var count = 0

    for (i in 1..n) {
        val chars = i.toString()
        val sentou = chars.first().toString().toInt()
        val matubi = chars.last().toString().toInt()

        if (matubi == 0) continue

        if (matubi < top) {
            count += p1
        } else if (matubi > top) {
            count += p2
        } else {
            count += p3 + p2
            if (sentou <= bottom) {
                count += 1
            }
        }


        if ((matubi.toString() + sentou.toString()).toInt() < n) {
            count += 1
        }

        if (sentou == matubi) {
            count += 1
        }
    }

    print(count)

}