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.*;
import java.io.*;
public class Main {
    static InputStreamReader r;
    public static void main(String[] args) throws Exception {
        r = new InputStreamReader(System.in);
        long N = nextInt();
        long rdN = N / 10 * 10;
        long count = 0;
        for (long i = rdN + 1; i <= N; i++) {
            String si = "" + i;
            long i_fd = Integer.parseInt(si.substring(0, 1));
            long i_ld = Integer.parseInt(si.substring(si.length() - 1, si.length()));
            for (long j = 1; j <= i; j++) {
                String sj = "" + j;
                long j_fd = Integer.parseInt(sj.substring(0, 1));
                long j_ld = Integer.parseInt(sj.substring(sj.length() - 1, sj.length()));
                if (i_fd == j_ld && i_ld == j_fd) {
                    if (i == j) {
                        count++;
                    } else {
                        count += 2;
                    }
                }
            }
        }

        long ans = N < 10 ? count : rdN * rdN / 100 + 8 + count;
        System.out.println(ans);
    }

    public static String nextString() throws Exception {
        String res = "";
        while (true) {
            int c = r.read();
            if (c == 32 || c == 10 || c == -1) {
                break;
            }
            res += (char)c;
        }
        return res;
    }

    public static int nextInt() throws Exception {
        return Integer.parseInt(nextString());
    }

    public static long nextLong() throws Exception {
        return Long.parseLong(nextString());
    }

    public static double nextDouble() throws Exception {
        return Double.parseDouble(nextString());
    }
}