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.*;
public class Main {
    public static void main(String[] args) {
        final int number = new Scanner(System.in).nextInt();
        int[][] array = new int[10][10];
        /*
        - 123456789
        1 2
        2
        3
        4
        5
        6
        7
        8
        9
         */
        for (int i = 1; i <= number; i++) {
            int start = i;
            while(start >= 10) {
                start /= 10;
            }
            int end = i % 10;
            array[start][end]++;
        }
        long answer = 0;
        for(int i = 1; i <= 9; i++) {
            for(int j = 1; j <= 9; j++) {
                answer += array[i][j] * array[j][i];
            }
        }
        System.out.println(answer);
    }
}