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)

n = gets.to_i

divisor = 1000000007

dp = Array.new(n+1) { Array.new(4, 0) }
dp[1] = [0, 1, 1, 8]

1.upto(n-1) do |i|

  dp[i+1][0] = (dp[i][0]*10 + dp[i][1] + dp[i][2]) % divisor
  dp[i+1][1] = (dp[i][1]*9 + dp[i][3]) % divisor
  dp[i+1][2] = (dp[i][2]*9 + dp[i][3]) % divisor
  dp[i+1][3] = (dp[i][3]*8) % divisor

end

# dp.each do |a|
#   p a
# end

puts dp.last.first