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)

fun main(args: Array<String>) {
    val mod = 1000000007L
    val n = getInt()
    val m = Array<LongArray>(3) {
        LongArray(n + 1) { 0L }
    }

    m[0][1] = 8L
    m[1][1] = 2L
    m[2][1] = 0L
    (2 .. n).forEach { i ->
        m[0][i] = m[0][i - 1] * 8 % mod
        m[1][i] = (m[0][i - 1] * 2 + m[1][i - 1] * 9) % mod
        m[2][i] = (m[1][i - 1] + m[2][i - 1] * 10) % mod
    }
    println(m[2][n])
}

fun getInt() = readLine()!!.toInt()