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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Diagnostics;

namespace AtCoder
{
    class Program
    {
        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }

        static int Count(int a, int b, int N)
        {
            int cnt = (a == b && N >= a) ? 1 : 0;
            int m = 1;
            while (true)
            {
                a *= 10;
                if (a + b > N)
                {
                    break;
                }
                else if (a + (m - 1) * 10 + b <= N)
                {
                    cnt += m;
                }
                else
                {
                    int n = (N / 10) % 10;
                    cnt += (b < N % 10) ? n + 1 : n;
                }
                m *= 10;
            }
            return cnt;
        }

        static long Solve(int N)
        {
            long sum = 0;
            for (int i = 1; i <= 9; ++i)
            {
                for (int j = 1; j <= 9; ++j)
                {
                    sum += Math.BigMul(Count(i, j, N), Count(j, i, N));
                }
            }
            return sum;
        }

        static void Main(string[] args)
        {
            int N = ReadInt();
            Console.WriteLine(Solve(N));
        }
    }
}