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;

class Program
{
    static void Main(string[] args)
    {
        var input =int.Parse(Console.ReadLine());
        var dict = new Dictionary<int, Dictionary<int, int>>();

        for (var i = 0; i <= 9; i++)
        {
            dict.Add(i, new Dictionary<int, int>());
            for(var j = 0; j <= 9; j++)
            {
                dict[i].Add(j, 0);
            }
        }

        for (var i = 1; i <= input; i++)
        {
            var str = i.ToString().ToCharArray();
            dict[int.Parse(str[0].ToString())][int.Parse(str[str.Length - 1].ToString())] += 1;
        }

        var ans = 0;

        for (var i = 1; i <= 9; i++)
        {
            for (var j = 0; j <= 9; j++)
            {
                ans += dict[i][j] * dict[j][i];
            }
        }


        Console.WriteLine(ans);

        Console.ReadLine();
    }


}