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: Accepted)

import java.util.Scanner;
 
public class Main {
 
	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		int N = scanner.nextInt();
		int result = 0;
		for (int i = 1; i <= 9; i++)
			for (int j = 1; j <= 9; j++) {
				result += num(N, i, j) * num(N, j, i);
			}
		System.out.println(result);
	}
 
	static int num(int max, int head, int tail) {
		int result = 0;
 
		for (int i = 1; i <= max; i++)
			if (i % 10 == tail && head(i) == head)
				result++;
 
		return result;
	}
 
	static int head(int i) {
		while (i > 9) {
			i /= 10;
		}
		return i;
	}
}