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)

my $N = <>;chomp $s;

if($N==1){
    print "0";exit;
}

my $mod = 10**9+7;

my $count =0;
my $non=8;
my $zero=1;
my $nine=1;

for($i=1;$i<$N;$i++){
    $count = ($count *10 + $zero + $nine)%$mod;
    $zero = ($zero*9 + $non)%$mod;
    $nine = ($nine*9 + $non)%$mod;
    $non  = ($non *8)%$mod;
}

print "$count";