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: Wrong Answer)

fun main() {
    val n = readLine()?.toLong() ?: return
    val m = (1e9 + 7).toLong()
    if (n == 1L) {
        println("0")
        return
    }
    var a = 1L
    var o = 1L
    var t = 1L
    repeat(n.toInt()) {
        a = a * 10L % m
        o = o * 9L % m
        t = t * 8L % m
    }
    a = (a - o - o + t) % m
    println(a.toString())
}