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: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;


namespace AtCoder
{
	class Program
	{
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            int[,] tmp = new int[10,10];
            for(int i = 0; i < N; i++)
            {
                int first, last;
                if (i > 99999) first = i / 100000;
                else if (i > 9999) first = i / 10000;
                else if (i > 999) first = i / 1000;
                else if (i > 99) first = i / 100;
                else if (i > 9) first = i / 10;
                else first = i;
                last = i % 10;
                tmp[first, last]++;
            }
            long ans = 0;
            for (int i = 0; i < N; i++)
            {
                int first, last;
                if (i > 99999) first = i / 100000;
                else if (i > 9999) first = i / 10000;
                else if (i > 999) first = i / 1000;
                else if (i > 99) first = i / 100;
                else if (i > 9) first = i / 10;
                else first = i;
                last = i % 10;
                ans += tmp[last,first];
            }
            Console.WriteLine(ans-1);
            Console.WriteLine();
            
            Console.ReadLine();
        }
    }
    
}