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: Accepted)

<?php
 fscanf(STDIN,"%d",$n);
 $mod = 10**9+7;

 function P($a,$n){
   global $mod;
   $re = 1;
   for($i=1;$i<=$n;$i++){
     $re = $re*$a%$mod;
   }
   return $re;
 }
 
 $ans = (P(10,$n)-(2*P(9,$n)-P(8,$n)));
 $ans %= $mod;
 $ans = ($ans+$mod)%$mod;
 echo $ans;