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

class Program
{
    static void Main(string[] args) {
#if DEBUG
        MyDebugger.Test(process, "../TextFile1.txt");
        //MyDebugger.Test(process, "../TextFile2.txt");
        //MyDebugger.MakeTestCase("../TextFile2.txt");
#else
        object ret = process(new StreamReader(Console.OpenStandardInput()));
        Console.WriteLine(ret);
#endif
    }

    static void Write(object obj) {
#if DEBUG
        Debug.Write(obj.ToString());
#else
        Console.Write(obj.ToString());
#endif
    }

    static object process(TextReader input) {
        var n = int.Parse(input.ReadLine());

        var tbl = new int[10][];

        for (int i = 0; i < tbl.Length; i++)
            tbl[i] = new int[10];

        for (int i=1; i<=n; i++) {
            var s = i.ToString();
            tbl[s.First() - '0'][s.Last() - '0'] += 1;
        }

        long c = 0;
        for (int i = 0; i <= 9; i++) {
            for (int j = 0; j <= 9; j++) {
                c += tbl[i][j] * tbl[j][i];
            }
        }

        return c;
    }

}