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)

import java.util.*

fun main() {
    val pw = java.io.PrintWriter(System.out)
    Problem.solve(Scanner(System.`in`), pw)
    pw.flush()
}

object Problem {
    val MOD = 1000000007L
    fun solve(sc: Scanner, pw: java.io.PrintWriter) {
        val N = sc.next().toInt()
        var a = 1L
        repeat(N) {
            a *= 10
            a %= MOD
        }
        var c = 1L
        repeat(N) {
            c *= 8
            c %= MOD
        }
        a += c
        a %= MOD

        var b = 1L
        repeat(N) {
            b *= 9
            b %= MOD
        }
        b *= 2
        b %= MOD

        a -= b
        a %= MOD
        if (a < 0) a += MOD
        pw.println(a)

    }
}