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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApp15
{
    class Class345
    {
        static void Main()
        {
            int N = int.Parse(Console.ReadLine());
            var A = new int[10, 10];
            long ans = 0;
            for(int i = 1; i <= N; i++)
            {
                int l = i.ToString()[0] - '0';
                int r = i % 10;
                A[l, r] += 1;
            }
            for(int i = 1; i < 10; i++)
            {
                for(int j = i; j < 10; j++)
                {
                    ans += A[i, j] * A[j, i];
                    if (i != j)
                        ans += A[j, i] * A[i, j];
                }
            }
            Console.WriteLine(ans);
        }
    }
    
}