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.HashMap;
import java.util.Map;
import java.util.Map.Entry;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		try (Scanner sc = new Scanner(System.in)) {
			long n = sc.nextLong();
			int result = 0;
			Map<Integer, Map<Integer, Integer>> map = new HashMap<>();
			for (int i = 1; i <= n; i++) {
				String ist = String.valueOf(i);
				int first = Integer.parseInt(ist.substring(0, 1));
				int last = Integer.parseInt(ist.substring(ist.length() - 1, ist.length()));
				Map<Integer, Integer> innerMap = map.get(first);
				if (innerMap == null) {
					innerMap = new HashMap<>();
					map.put(first, innerMap);
				}
				if (innerMap.get(last) == null) {
					innerMap.put(last, 0);
				}
				innerMap.put(last, innerMap.get(last) + 1);
			}
			for (Entry<Integer, Map<Integer, Integer>> entry : map.entrySet()) {
				for (Entry<Integer, Integer> innerEntry : entry.getValue().entrySet()) {
					if (map.get(innerEntry.getKey()) != null) {
						Integer wkValue = map.get(innerEntry.getKey()).get(entry.getKey());
						if (wkValue != null) {
							result = result + (innerEntry.getValue() * wkValue);
						}
					}
				}
			}
			System.out.println(result);
		}
	}
}