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: Time Limit Exceeded)

using System;

public class AtCoderD
{
    static void Main()
    {
        int n = int.Parse(Console.ReadLine());

        int[,] calcResults = new int[10, 10];
        for (int i = 0; i <= 9; i++)
        {
            for (int j = 0; j <= 9; j++)
            {
                calcResults[i, j] = -1;
            }
        }

        int answer = 0;
        for (int i = 0; i <= 9; i++)
        {
            string iStr = i.ToString();
            for (int j = 0; j <= 9; j++)
            {
                string jStr = j.ToString();
                int calcA;
                if (calcResults[i, j] != -1)
                {
                    calcA = calcResults[i, j];
                }
                else
                {
                    calcA = calc(iStr, jStr, n);
                }
                int calcB;
                if (calcResults[j, i] != -1)
                {
                    calcB = calcResults[j, i];
                }
                else
                {
                    calcB = calc(jStr, iStr, n);
                }
                answer += calcA * calcB;
            }
        }
        Console.WriteLine(answer);
    }

    static int calc(string start, string end, int n)
    {
        int ret = 0;
        for (int i = 1; i <= n; i++)
        {
            string str = i.ToString();
            if (str.StartsWith(start) && str.EndsWith(end))
            {
                ret++;
            }
        }
        return ret;
    }
}