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 powerMod(x: Int, n: Int, mod: Int): Int = when {
    n == 0 -> 1
    n % 2 == 1 -> ((powerMod(x, n - 1, mod).toLong() * x.toLong()) % mod).toInt()
    else -> {
        val tmp = (powerMod(x, n / 2, mod) % mod).toLong()
        ((tmp * tmp) % mod).toInt()
    }
}

fun main() {
    val n = readLine()!!.toInt()
    val mod = 1_000_000_000 + 7
    val res = powerMod(10, n, mod) - (powerMod(9, n, mod) + powerMod(9, n, mod) - powerMod(8, n, mod)) % mod
    println((res + mod) % mod)
}