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.Diagnostics;
using System.Linq;

internal static class CR
{
    public static string Get() { return Console.ReadLine(); }
    public static IEnumerable<string> GetTexts() { return Console.ReadLine().Split(' '); }
    public static int GetInteger() { return int.Parse(Console.ReadLine()); }
    public static IEnumerable<int> GetIntegers() { return Console.ReadLine().Split(' ').Select(x => int.Parse(x)); }
}

namespace AtCoderBeginnerContest
{
    internal class Program
    {
        public static int N { get; private set; }

        private static void Main() { var r = GetResult(); Debug.WriteLine(r); Console.WriteLine(r); }

        private static object GetResult()
        {
            N = CR.GetInteger();

            return Solve_2();
        }

        private static object Solve_2()
        {
            var count = 0;

            for (int i = 1; i < 10; i++)
            {
                count += NewMethod(i);
            }

            var Xs = new List<XX>();
            for (int i = 1; i < 10; i++)
            {
                for (int j = 1; j < 10; j++)
                {
                    if (i == j) continue;

                    Xs.Add(new XX { First = i, Last = j, Count = X(i, j) });
                }
            }

            for (int i = 1; i < 10; i++)
            {
                for (int j = i + 1; j < 10; j++)
                {
                    count += Xs.First(x => x.First == i && x.Last == j).Count
                        * Xs.First(x => x.First == j && x.Last == i).Count
                        *2;
                }
            }

            return count;
        }
        class XX
        {
            public int First { get; set; }
            public int Last { get; set; }
            public int Count { get; set; }
        }
        private static int X(int o_1, int o_2)
        {
            var count = 0;
            if (o_1 + o_2 * 10 <= N)
            {
                count++;
            }
            for (int i = 0; i < 10; i++)
            {
                if (int.Parse(o_1.ToString() + i.ToString() + o_2.ToString()) <= N)
                {
                    count++;
                }
            }
            for (int i = 0; i < 100; i++)
            {
                if (int.Parse(o_1.ToString() + string.Format("{0:D2}", i) + o_2.ToString()) <= N)
                {
                    count++;
                }
            }
            for (int i = 0; i < 1000; i++)
            {
                if (int.Parse(o_1.ToString() + string.Format("{0:D3}", i) + o_2.ToString()) <= N)
                {
                    count++;
                }
            }
            for (int i = 0; i < 10000; i++)
            {
                if (int.Parse(o_1.ToString() + string.Format("{0:D4}", i) + o_2.ToString()) <= N)
                {
                    count++;
                }
            }
            return count;
        }

        private static int NewMethod(int one)
        {
            var count = 0;
            if (one <= N)
            {
                count++;
            }
            if (one + one * 10 <= N)
            {
                count++;
            }
            for (int i = 0; i < 10; i++)
            {
                if (int.Parse(one.ToString() + i.ToString() + one.ToString()) <= N)
                {
                    count++;
                }
            }
            for (int i = 0; i < 100; i++)
            {
                if (int.Parse(one.ToString() + string.Format("{0:D2}", i) + one.ToString()) <= N)
                {
                    count++;
                }
            }
            for (int i = 0; i < 1000; i++)
            {
                if (int.Parse(one.ToString() + string.Format("{0:D3}", i) + one.ToString()) <= N)
                {
                    count++;
                }
            }
            for (int i = 0; i < 10000; i++)
            {
                if (int.Parse(one.ToString() + string.Format("{0:D4}", i) + one.ToString()) <= N)
                {
                    count++;
                }
            }
            return (int)Math.Pow(count, 2);
        }

        private static object Solve_1()
        {
            var count = 0;
            for (int i = 1; i <= N; i++)
            {
                for (int j = i; j <= N; j++)
                {
                    var istring = i.ToString();
                    var jstring = j.ToString();
                    if (istring.First() == jstring.Last() && istring.Last() == jstring.First())
                    {
                        if (i == j)
                        {
                            count++;
                        }
                        else
                        {
                            count += 2;
                        }
                    }
                }
            }

            return count;
        }
    }
}