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 Haskell (GHC 8.8.3) (judge verdict: Accepted)

m :: Int
m = 1000000007

fpm :: Int -> Int -> Int
fpm a e
  | e == 0 = 1
  | odd e = p * p `mod` m * a `mod` m
  | otherwise = p * p `mod` m
  where
  p = fpm a (e `div` 2)

main :: IO ()
main = do
  n <- read <$> getLine
  putStrLn $ show $ (fpm 10 n + m - (fpm 9 n) * 2 + fpm 8 n) `mod` m