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: Runtime Error)

<?php

$n = (int) trim(fgets(STDIN));

$a = $b = [];
for ($i = 1; $i <= $n; $i++) {
    $target = (string)$i;

    $last = $target[mb_strlen($target) - 1];
    if ($last === '0') {
        continue;
    }

    $a[] = "$target[0]$last";
    $b[] = "$last$target[0]";
}

$valuesA = array_count_values($a);
$valuesB = array_count_values($b);

$ans = 0;

foreach ($valuesA as $k => $v) {
    if (isset($valuesB[$k])) {
        $ans += $v * $valuesB[$k];
    }
}

echo $ans;