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)

main = getLine >>= print . compute . read

base = 10^9+7

compute :: Int -> Int
compute n = loop n 10 9 8 1 1 1

loop 0 _ _ _ acc10 acc9 acc8 = (acc10 + acc8 - 2 * acc9) `mod` base
loop n pow10 pow9 pow8 acc10 acc9 acc8
  | odd n = loop1 (m acc10 pow10) (m acc9 pow9) (m acc8 pow8)
  | True  = loop1    acc10           acc9          acc8
  where
    loop1 = loop (n `div` 2) (p pow10) (p pow9) (p pow8)

p x = m x x
m x y = x*y `mod` base
{-
0から9任意 = 10^n : A
0から8任意 = 9^n : B   A-B = 9が1つはある
1から9任意 = 9^n : C   A-C = 0が1つはある
1から8任意 = 8^n : D   A-(B+C-D) = 求めるもの
-}