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 Common Lisp (SBCL 2.0.3) (judge verdict: Wrong Answer)

(let* ((n (read))
    (strn (princ-to-string n))
    (ans 0))
    (loop for i below (expt 10 n) do
        (progn
            (if (not (null (find #\9 (princ-to-string i) :test #'equalp)))
                (if (> (parse-integer strn) (length (princ-to-string i)))
                    (incf ans)
                    (if (not (null (find #\9 (princ-to-string i) :test #'equalp)))
                        (incf ans)
                    )
                )
        )
        (setq ans (rem ans 1000000007))
        )
    )
    (princ ans)
)