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 PHP (5.6.30) (judge verdict: Accepted)

<?php

$maxNumber = preg_replace('/(\\r|\\n|\\r\\n)/', '',fgets(STDIN));

$classification = [];
for($i = 1; $i <= $maxNumber; $i ++) {
    $topNumber = substr($i, 0, 1);
    $bottomNumber = $i % 10;
    
    if(empty($classification[$topNumber])){
        $classification[$topNumber] = [];
    }
    if(empty($classification[$topNumber][$bottomNumber])){
        $classification[$topNumber][$bottomNumber] = 1;
    } else {
        $classification[$topNumber][$bottomNumber] ++;
    }
}

$result = 0;
for($i = 1; $i <= 9; $i++) {
    for($j = 1; $j <= 9; $j++) {
        if(empty($classification[$i][$j]) || empty($classification[$j][$i])){
            continue;
        }
        $result += $classification[$i][$j] * $classification[$j][$i];
    }
}

echo $result.PHP_EOL;