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: Accepted)

Scanf.scanf "%d" (fun n ->
    let z = 1_000_000_007 in
    let ( +@) a b = (a + b) mod z in
    let ( *@) a b = (a * b) mod z in

    let rec loop i d09 d0 d9 dn =
        if i = n then d09 else
            loop (i + 1) (d09 *@ 10 +@ d0 +@ d9) (d0 *@ 9 +@ dn) (d9 *@ 9 +@ dn) (dn *@ 8)
    in
    loop 0 0 0 0 1 |> Printf.printf "%d\n"
)