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 static System.Console;
using static System.Int32;
using static System.Math;
using System.Linq;
using System.Collections.Generic;

class Solution
{
    static void Main()
    {
    lb:
        var n = Parse(ReadLine());
        var dic = new Dictionary<KeyValuePair<int, int>, int>();
        for (int a = 1; a <= n; ++a)
        {
            var iti = a % 10;
            if (iti == 0) continue;
            int juu = a;
            while (10 <= juu) juu /= 10;
            var p = new KeyValuePair<int, int>(juu, iti);
            int val;
            if (dic.TryGetValue(p, out val))
            {
                dic[p] = val + 1;
            }
            else
            {
                dic[p] = 1;
            }
        }
        int result = 0;
        foreach (var pair in dic)
        {
            var key = new KeyValuePair<int, int>(pair.Key.Value, pair.Key.Key);
            int val;
            if (!dic.TryGetValue(key, out val)) continue;
            result += pair.Value * val;
        }
        WriteLine(result);
    }
}