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: Accepted)

<?php
fscanf(STDIN, '%d', $n);
$cnt = [];
for ($i = 0; $i < 10; $i++) {
    $cnt[] = array_fill(0, 10, 0);
}

for ($i = 1; $i <= $n; $i++) {
    $keta_last = $i % 10;
    $keta_first = intval(substr(strval($i), 0, 1));
    $cnt[$keta_last][$keta_first]++;
}
$ans = 0;
for ($i = 1; $i <= 9; $i++) {
    for ($j = 1; $j <= 9; $j++) {
        $ans += ($cnt[$i][$j] ?? 0) * ($cnt[$j][$i] ?? 0);
    }
}
echo $ans . PHP_EOL;