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 Perl (5.26.1) (judge verdict: Accepted)

#!/usr/bin/perl

my ($n) = map { $_ - 0 } split(/\s+/,<STDIN>);

my $md = 10 ** 9 + 7;

my $k1 = 1;
my $k2 = 1;
my $k3 = 1;

for(my $i=0;$i<$n;$i++){
  $k1 = ( $k1 * 10 ) % $md;
  $k2 = ( $k2 * 9 ) % $md;
  $k3 = ( $k3 * 8 ) % $md;
}

my $r = (10*$md + $k1 - 2 * $k2 + $k3) % $md;

print "$r\n";