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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;

class Program
{
    static void Main(string[] args)
    {
        var N = int.Parse(ReadLine());

        IEnumerable<int> GetNum(int a, int b)
        {
            var q = new Queue<int>();

            var v = 0;

            if (a == b)
            {
                v = a;
                yield return v;
            }

            v = a * 10 + b;
            q.Enqueue(v);
            yield return v;

            while(true)
            {
                v = q.Dequeue();
                v -= b;
                v *= 10;
                for (int i = 0; i <= 9; i++)
                {
                    var _v = v + (i * 10) + b;
                    q.Enqueue(_v);
                    yield return _v;
                }
            }
        }

        var pairCount = new int[10, 10];

        for (int i = 1; i <= 9; i++)
        {
            for (int j = 1; j <= 9; j++)
            {
                pairCount[i, j] = GetNum(i, j).TakeWhile(x => x <= N).Count();
            }
        }

        var ans = 0;

        for (int i = 1; i <= N; i++)
        {
            var iStr = i.ToString();
            var a = iStr[0] - '0';
            var b = iStr[iStr.Length - 1] - '0';

            ans += pairCount[b, a];
        }

        WriteLine(ans);
    }
}