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 PHP7 (7.0.15) (judge verdict: Time Limit Exceeded)

<?php
  fscanf(STDIN, "%d", $N);
  $count = 0;
 $j = 1;

for($i=1;$i<=$N;$i++){
    for($j=1;$j<=$N;$j++){
      $a = $i;
      $b = $j;
      
      if(substr($a, 0, 1) === substr($b, -1, 1) 
         && substr($b, 0, 1) === substr($a, -1, 1)){
       	$count++; 
        continue;
   //     echo $a. " ". $b."\n";
      }
    }    
  }
	echo $count;

  ?>