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 System.Text;
using System.Threading.Tasks;

namespace Contest_01_Valeo_P6
{
    class Program
    {

        static void Main(string[] args)
        {
            //while (true)
            //{
            //    Console.WriteLine("start problem");
                string input = Console.ReadLine();
                long n = long.Parse(input.Split(' ')[0]);
                long result = getNumberOfPairs(n);
                Console.WriteLine(result);
            //    Console.Write("press y to exit : ");
            //    if (Console.ReadLine() == "y")
            //        return;
            //}
        }

        /// <summary>
        /// in session
        /// construct map of occurances
        /// </summary>
        /// <param name="n"></param>
        /// <returns></returns>
        private static long getNumberOfPairs(long n)
        {
            long count = 0;
            List<List<long>> l = new List<List<long>>();
            for (int i = 1; i <= 10; i++)
            {
                List<long> intern = new List<long>();
                for (int j = 1; j <= 10; j++)
                {
                    intern.Add(0);
                }
                l.Add(intern);
            }
            for (long x = 1; x <= n; x++)
            {
                int startDigit = x.ToString().Select(c => int.Parse(c.ToString())).First();
                int endDigit = x.ToString().Select(c => int.Parse(c.ToString())).Last();
                
                l[startDigit][endDigit]++;
            }

            for (int i = 0; i < 10; i++)
            {
                count += l[i][i] *l[i][i];
                for (int j = i+1; j < 10; j++)
                {
                    count += 2 * l[i][j] * l[j][i];
                }
            }
            return count;
        }
    }
}