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

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long N = Long.parseLong(sc.nextLine());
        sc.close();
        long res = 0;
        Map<Map<Long, Long>, Long> pairMap = new HashMap<>();

        for (long i = 1; i <= N; i++) {
            Map<Long, Long> map = getFandLPair(i);
            Long count = pairMap.get(map);
            if (Objects.isNull(count)) {
                pairMap.put(map, 1L);
            } else {
                count++;
                pairMap.put(map, count);

            }
        }

        for (long i = 1; i <= N; i++) {
            Map<Long, Long> pMap = getFandLPair(i);
            Long key = pMap.keySet().iterator().next();
            Map<Long, Long> gMap = new HashMap<Long, Long>();
            gMap.put(pMap.get(key), key);
            Long count = pairMap.get(gMap);
            if (Objects.isNull(count)) {
                continue;
            }
            res += count;
        }

        System.out.println(res);
    }

    public static Map<Long, Long> getFandLPair(Long x) {
        Map<Long, Long> ret = new HashMap<>();
        String Z = x.toString();
        Long a = Long.parseLong(String.valueOf(Z.charAt(0)));
        Long b = Long.parseLong(String.valueOf(Z.charAt(Z.length() - 1)));
        ret.put(a, b);
        return ret;
    }

}