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 static Input;
using NX = System.Int64;


public class Prog
{
    public struct Pair { public int x, y; public Pair(int a, int b) { x = a; y = b; } }
    public static void Solve()
    {
        int N = NextInt();
        Dictionary<Pair, long> d = new Dictionary<Pair, NX>();
        long ans = 0;
        for (int x = 1; x <= N; x++)
        {
            if (x <= 9)
            {
                if (!d.ContainsKey(new Pair(x, x))) d[new Pair(x, x)] = 0;
                d[new Pair(x, x)]++;
                continue;
            }
            string s = x.ToString();
            int a = int.Parse(s[0].ToString());
            int b = int.Parse(s[s.Length - 1].ToString());
            if (!d.ContainsKey(new Pair(a, b))) d[new Pair(a, b)] = 0;
            d[new Pair(a, b)]++;
        }
        foreach (var e in d.Keys)
        {
            if (!d.ContainsKey(new Pair(e.y, e.x))) continue;
            ans += d[e] * d[new Pair(e.y, e.x)];
        }
        Console.WriteLine(ans);
    }
    public static long GCD(long a, long b)
    {
        if (a < b) GCD(b, a);
        long d = a % b;
        while (b != 0)
        {
            d = a % b;
            a = b;
            b = d;
        }
        return a;
    }
    public static long LCM(long a, long b)
    {
        return a / GCD(a, b) * b;
    }

    public static void Main()
    {
        var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);
        Solve();
        Console.Out.Flush();
        return;
    }
}

public class Input
{
    public const long MOD = 1000000007;
    public const int INF = 1000000007;
    private static Queue<string> q = new Queue<string>();
    private static void Confirm() { if (q.Count == 0) foreach (var s in Console.ReadLine().Split(' ')) q.Enqueue(s); }
    public static int NextInt() { Confirm(); return int.Parse(q.Dequeue()); }
    public static long NextLong() { Confirm(); return long.Parse(q.Dequeue()); }
    public static string NextString() { Confirm(); return q.Dequeue(); }
    public static double NextDouble() { Confirm(); return double.Parse(q.Dequeue()); }
    public static int[] LineInt() { return Console.ReadLine().Split(' ').Select(int.Parse).ToArray(); }
    public static long[] LineLong() { return Console.ReadLine().Split(' ').Select(long.Parse).ToArray(); }
    public static string[] LineString() { return Console.ReadLine().Split(' ').ToArray(); }
    public static double[] LineDouble() { return Console.ReadLine().Split(' ').Select(double.Parse).ToArray(); }
    public long Abs(long a, long b) => Math.Abs(a - b);
}