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 Go (1.14.1) (judge verdict: Accepted)

package main

import (
	"fmt"
)

const div = 1000000007

func Powmod(x, n int) int {
	res := 1
	for i := 0; i < n; i++ {
		res = (res * x) % div
	}
	return res
}

func main() {
	var n int
	fmt.Scan(&n)
	ans := Powmod(10, n) - 2*Powmod(9, n) + Powmod(8, n)
	ans %= div
	ans = (ans + div) % div
	fmt.Println(ans)
}