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: Runtime Error)

private fun readInt() = readLine()!!.toInt()

private fun readInts() = readLine()!!.split(' ').map { it.toLong() }

val Long.fact get() = (1..this).fold(1L) { acc, i -> acc * i }

fun c(n: Long, k: Long): Long {
    return n.fact/(k.fact * (n-k).fact)
}

fun main() {
    val n = readInt().toLong()
    val x = (1 until n).map { k-> c(n, k) }.sum()
    println(x % (1000000007L))
}