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 Kotlin (1.3.71) (judge verdict: Accepted)

val mod = (1e9 + 7).toInt()

fun main() {
  val n = readLine()!!.toLong()
  
  var res = pow(10, n)
  res = (res - pow(9, n) - pow(9, n) + mod + mod) % mod
  res = (res + pow(8, n)) % mod
  println(res)
}
 
fun pow(a:Long, n:Long):Long {
	var res = 1L
  	var a = a
  	var n = n
  	while(n > 0) {
    	if(n % 2 == 1L) res = (res * a) % mod  
      	n = n / 2
        a = (a * a) % mod
    }
  	return res
}