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 Scala (2.13.1) (judge verdict: Wrong Answer)

import io.StdIn.{readInt, readLong}
object Main extends App {
  val n = readInt
  
  // general expression 10^n-9^n-9^n+8^n
  val divisor = 1000000000L+7L
  var num1 = 10L
  var num2 = 9L
  var num3 = 8L

  for (_ <- 1 until n) {
    num1 *= 10
    num1 %= divisor
    num2 *= 9
    num2 %= divisor
    num3 *= 8
    num3 %= divisor
  }

  println(num1-num2-num2+num3)

}