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.ComponentModel;
using System.ComponentModel.DataAnnotations;
using System.Data.SqlTypes;
using System.Linq;
using System.Text;
using System.Threading;

class Program
{
    static int INF = 10000000;
    static void Main(string[] args)
    {
        int keta = 1;
        int nextKeta = 10;
        int n = int.Parse(Console.ReadLine());
        var dic = new Dictionary<(int x , int y),int>();
        for(int i = 1; i <= n; i++)
        {
            if(i == nextKeta)
            {
                keta *= 10;
                nextKeta *= 10;
            }
            int a = i / keta;
            int b = i % 10;
            if (!dic.ContainsKey((a , b)))dic.Add((a, b), 1);
            else dic[(a,b)]++;
        }
        int sum = 0;
        foreach(var ele in dic.Keys)
        {
            int x = ele.y;
            int y = ele.x;
            if (!dic.ContainsKey((x,y)))continue;
            sum += dic[ele] * dic[(x,y)];
        }
        Console.WriteLine(sum);
    }

}