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)

binpow a b mmod
  | b == 0    = 1
  | otherwise =
    if b `mod` 2 == 1 then
      res `mod` mmod * res `mod` mmod * a `mod` mmod
    else
      res `mod` mmod * res `mod` mmod
        where res = binpow a (b `div` 2) mmod

main = do
  li <- getLine
  let n = read li :: Integer
  let mmod = 10^9+7
  print $ ((\x -> (x + mmod) `mod` mmod) :: Integer -> Integer)
    $ (binpow 10 n mmod) - ((*2) $ binpow 9 n mmod) + (binpow 8 n mmod)