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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.Scanner;

public class Main {

    private static int f(int i, int j, int n) {
        int r = 0;
        for (int k = 1; k <= n; k++) {
            String s = Integer.toString(k);
            if (Integer.parseInt(s.substring(0, 1)) == i && Integer.parseInt(s.substring(s.length() - 1)) == j)
                r++;
        }
        return r;
    }

    public static void main(String[] args) {
        try (Scanner scanner = new Scanner(System.in)) {
            int n = Integer.parseInt(scanner.next());
            int r = 0;
            for (int i = 0; i < 10; i++) {
                for (int j = 0; j < 10; j++) {
                    r += f(i, j, n) * f(j, i, n);
                }
            }
            System.out.println(r);
        }
    }

}