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 OCaml (4.10.0) (judge verdict: Wrong Answer)

let () =
  Scanf.scanf "%d\n" @@ fun n ->
  let rec powmod x y ans = 
  	if y = 0 then ans else powmod x (y-1) (ans * x mod 1000000007) in
  Printf.printf "%d\n"
    (((powmod 10 n 1) - 2 * (powmod 9 n 1) + (powmod 8 n 1)) mod 1000000007)