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: Wrong Answer)

N = gets.to_i

# $stdout = File.open(File::NULL, "w")

def main
  max = 10 ** 9 + 7
  all = 1
  zero = 1
  nine = 1
  zn = 1
  N.times.each do
    all = all * 10 % max
    zero = zero * 9 % max
    nine = nine * 9 % max
    zn = zn * 8 % max
  end
  return all - zero - nine + zn
end

STDOUT.puts main