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 Ruby (2.7.1) (judge verdict: Accepted)

def gs() gets.chomp end
def gi() gets.to_i end
def gsmi() gets.chomp.split.map(&:to_i) end
def ang(n) Array.new(n){gsmi} end
def debug(k,v) puts "#{k}: #{v}" end
def desc(ar) ar.sort!{|x,y|y<=>x} end
def min(a,b) a<=b ? a : b end
def max(a,b) a>=b ? a : b end
def sum(ar) ar.inject(:+) end

$stdin = File.open('input.txt') if File.exist?('input.txt')
mod = 10**9 + 7
n = gi

(puts 0;exit) if n==1

puts (10**n - 9**n - 9**n + 8**n)%mod