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.Collections.Generic;
using System;

public class Hello
{
    public static void Main()
    {
        var d = new Dictionary<string, int>();
        var n = int.Parse(Console.ReadLine().Trim());
        for (int i = 1; i <= n; i++)
        {
            var its = i.ToString();
            var k = "" + its[0] + its[its.Length - 1];
            if (d.ContainsKey(k)) d[k]++;
            else d[k] = 1;
        }
        getAns(n, d);
    }
    static void getAns(int n, Dictionary<string, int> d)
    {
        var ans = 0;
        foreach (var x in d)
            if (x.Key[x.Key.Length - 1] != '0')
            {
                var nk = "" + x.Key[x.Key.Length - 1] + x.Key[0];
                if (d.ContainsKey(nk)) ans += x.Value * d[nk];
            }
        Console.WriteLine(ans);
    }
}