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

$N = fgets(STDIN);


$MOD = pow(10, 9) + 7;

$a = mypow(10, $N);
$b = mypow(9, $N);
$c = mypow(8, $N);

$ans = ($a - 2 * $b + $c) % $MOD;

echo $ans;

function mypow($b, $p)
{
    $mod = pow(10, 9) + 7;
    $res = 1;
    for ($i = 0; $i < $p; $i++) {
        $res = ($res * $b) % $mod;
    }
    return $res;
}


?>