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.Linq;
using System.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
		int n = int.Parse(Console.ReadLine());
        
        int[,] A = new int[10,10]; //n以下の数字で先頭がiで、末尾がjの数字の個数を格納
        for(int k=1;k<=n;k++){
            string strK = k.ToString();
            int start = int.Parse(strK.Substring(0,1));
            int end = int.Parse(strK.Substring(strK.Length-1,1));
            A[start,end]++;
        }
        
        long count = 0;
        for(int i=0;i<10;i++){
            for(int j=0;j<10;j++){
                count += (long)A[i,j] * (long)A[j,i];
                //Console.Write(A[i,j] + " ");
            }
            //Console.WriteLine("");
        }
        Console.WriteLine(count);
	}
}