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: Runtime Error)

<?php
  
  $num = intval(trim(fgets(STDIN)));
  
  if($num === 2){
    echo 2;
  }else if( $num < 2){
    echo 0;
  else{
    
    $answer = ( $num * ($num - 1) * pow(10,$num) ) % ( pow(10,9) + 7);

    echo $answer;
    
  }
    
  
  

  ?>