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.Linq;

namespace AtCoderBeginnerContest152
{
	class Program
	{
		private const int ModNum = 1000000007;

		static void Main(string[] args)
		{
			var number = int.Parse(Console.ReadLine());
			var cij = new int[10, 10];

			for (var i = 1; i <= number; i++)
			{
				cij[HighestNumber(i), i % 10]++;
			}

			var result = 0;
			for (var i = 0; i < 10; i++)
			{
				for (var j = 0; j < 10; j++)
				{
					result += cij[i, j] * cij[j, i];
				}
			}

			Console.WriteLine(result);
		}

		private static int HighestNumber(int num)
		{
			var result = num / 1;
			while (result >= 10)
			{
				result /= 10;
			}
			return result;
		}
	}
}