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)

#|
------------------------------------
|               Utils               |
------------------------------------
|#


(eval-when (:compile-toplevel :load-toplevel :execute)
  (defparameter OPT
    #+swank '(optimize (speed 3) (safety 2))
    #-swank '(optimize (speed 3) (safety 0) (debug 0)))
  #+swank (progn (ql:quickload '(:cl-debug-print :fiveam))
                 (shadow :run)
                 (use-package :fiveam)))
#+swank (cl-syntax:use-syntax cl-debug-print:debug-print-syntax)

#-swank
(unless (member :child-sbcl *features*)
  (quit
   :unix-status
   (process-exit-code
    (run-program *runtime-pathname*
                 `("--control-stack-size" "128MB"
                   "--noinform" "--disable-ldb" "--lose-on-corruption" "--end-runtime-options"
                   "--eval" "(push :child-sbcl *features*)"
                   "--script" ,(namestring *load-pathname*))
                 :output t :error t :input t))))


(defconstant +mod+ 1000000007)


(defmacro define-int-types (&rest bits)
  `(progn
     ,@(mapcar (lambda (b) `(deftype ,(intern (format nil "INT~a" b)) () '(signed-byte ,b))) bits)
     ,@(mapcar (lambda (b) `(deftype ,(intern (format nil "UINT~a" b)) () '(unsigned-byte ,b))) bits)))

(define-int-types 2 4 8 16 32 64)


(declaim (inline println))
(defun println (obj &optional (stream *standard-output*))
  (let ((*read-default-float-format* 'double-float))
    (prog1
        (write obj :stream stream)
      (fresh-line stream))))


(defmacro safe-sort (list test &key (key #'identity))
  `(progn
    (declaim (inline sort sb-impl::stable-sort-list))
    (sort (copy-seq ,list) ,test :key ,key)))


(defmacro read-numbers-to-list (size)
  `(loop repeat ,size collect (read)))


(defmacro read-numbers-to-array (size)
  (let ((i (gensym))
        (arr (gensym)))
    `(let ((,arr (make-array ,size
                             :element-type 'fixnum)))
       (declare ((array fixnum 1) ,arr))
       (loop for ,i of-type fixnum below ,size do
            (setf (aref ,arr ,i) (read))
          finally
            (return ,arr)))))

(defmacro read-characters-to-board (row-size column-size)
  (let ((board (gensym))
        (r (gensym))
        (c (gensym))
        (tmp (gensym)))
    `(let ((,board (make-array '(,row-size ,column-size) :element-type 'character :adjustable nil)))
       (dotimes (,r ,row-size ,board)
         (let ((,tmp (read-line)))
           (dotimes (,c ,column-size)
             (setf (aref ,board ,r ,c) (char ,tmp ,c))))))))

(defmethod princ-for-each-line ((sequence list))
  (format t "~{~a~&~}" sequence))

(defmethod princ-for-each-line ((sequence vector))
  (loop for i below (length sequence) do
       (princ (aref sequence i))
       (fresh-line)))

(defun unwrap (list)
  (format nil "~{~a~^ ~}" list))



(defmacro with-buffered-stdout (&body body)
  (let ((out (gensym)))
    `(let ((,out (make-string-output-stream :element-type 'base-char)))
       (let ((*standard-output* ,out))
         ,@body)
       (write-string (get-output-stream-string ,out)))))





#|
------------------------------------
|               Body               |
------------------------------------
|#


(defun my-expt (base n)
  (loop repeat n with res = 1 do
       (setf res (mod (* res base) +mod+))
     finally
       (return res)))

(defun solve (n)
  (let((tmp (+ (- (my-expt 10 n)
                  (my-expt 9 n)
                  (my-expt 9 n))
               (my-expt 8 n))))
    (if (< tmp 0)
        (+ tmp +mod+)
        tmp)))


(defun main ()
  (declare #.OPT)
  (let ((n (read)))
    (format t "~a~&" (solve n))))

#-swank (main)