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
//error_reporting(0);
$N = trim(fgets(STDIN));
//list($a,$b) = explode(" ",trim(fgets(STDIN)));
//$P = explode(" ",trim(fgets(STDIN)));
//$a = array_map('intval',explode(" ",trim(fgets(STDIN))));

for($i=1;$i<=$N;$i++){
    $start = substr($i,0, 1);
    $end = substr($i, -1);
    if($end == 0){
        continue;
    }
    @$map[$start][$end] += 1;
}
$ans=0;
for($i=1;$i<=$N;$i++){
    $start = substr($i,0, 1);
    $end = substr($i, -1);
    if($end == 0){
        continue;
    }
    $ans+=$map[$end][$start];
}
printf("%d\n",$ans);