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;
using System.Text;
using System.Threading.Tasks;

namespace abc152_d
{
  class Program
  {
    static void Main(string[] args)
    {
      var N = CIn.ReadInt();

      var a = new int[10, 10];

      for (int i = 1; i <= N; i++)
      {
        var t = i.ToString()[0] - '0';
        var b = i % 10;
        a[t, b]++;
      }

      var ans = 0;

      for (int i = 0; i <= N; i++)
      {
        if (i % 10 != 0)
        {
          var t = i.ToString()[0] - '0';
          var b = i % 10;

          ans += a[b, t];
        }
      }

      Console.WriteLine(ans);
    }
  }

  static class CIn
  {
    private static readonly Queue<string> fieldBuffer = new Queue<string>();

    public static string Read()
    {
      if (fieldBuffer.Count == 0)
      {
        foreach (var field in Console.ReadLine().Split())
        {
          fieldBuffer.Enqueue(field);
        }
      }
      return fieldBuffer.Dequeue();
    }

    public static int ReadInt() => int.Parse(Read());
    public static long ReadLong() => long.Parse(Read());
    public static double ReadDouble() => double.Parse(Read());

    public static string[] ReadStringArray(long n)
    {
      var array = new string[n];
      for (var i = 0L; i < n; i++)
      {
        array[i] = Read();
      }
      return array;
    }

    public static int[] ReadIntArray(long n)
    {
      var array = new int[n];
      for (var i = 0L; i < n; i++)
      {
        array[i] = ReadInt();
      }
      return array;
    }

    public static long[] ReadLongArray(long n)
    {
      var array = new long[n];
      for (var i = 0L; i < n; i++)
      {
        array[i] = ReadLong();
      }
      return array;
    }

    public static double[] ReadDoubleArray(long n)
    {
      var array = new double[n];
      for (var i = 0L; i < n; i++)
      {
        array[i] = ReadDouble();
      }
      return array;
    }

    public static char[,] ReadCharMatrix(long h, long w)
    {
      var array = new char[h, w];
      for (var i = 0L; i < h; i++)
      {
        var l = Console.ReadLine().ToCharArray();
        for (var j = 0L; j < w; j++)
        {
          array[i, j] = l[j];
        }
      }
      return array;
    }
  }
}