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: Accepted)


import scala.io.StdIn

object Main extends App {
  val n= StdIn.readInt()
  val all = BigInt(10).pow(n)
  val withoutANuber = BigInt(9).pow(n)
  val withoutTwoNumber = BigInt(8).pow(n)

  val ans = all - (2 * withoutANuber - withoutTwoNumber)
  val mod = BigInt(10).pow(9) + 7
  println(ans % mod)
}