Problem:
Score : 300 points

Problem Statement

How many integer sequences A_1,A_2,\ldots,A_N of length N satisfy all of the following conditions?

0 \leq A_i \leq 9

There exists some i such that A_i=0 holds.

There exists some i such that A_i=9 holds.

The answer can be very large, so output it modulo 10^9 + 7.

Constraints

1 \leq N \leq 10^6

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

Print the answer modulo 10^9 + 7.

Sample Input 1

2

Sample Output 1

2

Two sequences \{0,9\} and \{9,0\} satisfy all conditions.

Sample Input 2

1

Sample Output 2

0

Sample Input 3

869121

Sample Output 3

2511445

Solution in PHP (7.4.4) (judge verdict: Wrong Answer)

<?php 

$mod = 10**9+7;

function carcu(int $x, int $y){
    $mod = 10**9+7;
    $num = 1;
    for($i=0;$i<$y;$i++){
        $num=$num*$x%$mod;
    }
    return $num;
}

$n = fgets(STDIN);

$ans = carcu(10,$n) - carcu(9,$n) - carcu(9,$n) + carcu(8,$n);
$ans%=$mod;
echo $ans."\n";