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

        int order = 0;
        int tmpN = n;
        while (tmpN != 0)
        {
            order++;
            tmpN = tmpN / 10;
        }

        int answer = 0;

        for (int a = 1; a <= n; a++)
        {
            string str = a.ToString();
            string first = str.Substring(0, 1);
            string last = str.Substring(str.Length - 1, 1);
            for (int b = 1; b <= n; b++)
            {
                string targetStr = b.ToString();
                string targetFirst = targetStr.Substring(0, 1);
                string targetLast = targetStr.Substring(targetStr.Length - 1, 1);
                if(first.Equals(targetLast) && last.Equals(targetFirst))
                {
                    answer++;
                }
            }
        }

        //for (int a = 1; a <= n; a++)
        //{
        //    for (int i = 1; i <= order; i++)
        //    {
        //        if (i == 1)
        //        {
        //            answer++;
        //        }
        //        else if (i == order)
        //        {

        //        }
        //        else
        //        {
        //            answer += (int)(Math.Pow(10, order - 2));
        //        }
        //    }
        //}

        Console.WriteLine(answer);
    }
}