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: Wrong Answer)

package main
 
import (
	"fmt"
)
 
func main() {
	var n int
	fmt.Scanf("%d", &n)

	var ans int64 = 0
	if n<2{
		ans = 0
	} else {
		var t int64 = 1
		var u int64 = 1
		var s int64 = 1
		for i:= 0; i < n; i++{
			s = s * 9 % 1000000007
			t = t * 8 % 1000000007
			u = u * 10 % 1000000007
		}


		ans = u - s - s + t

	}

	ans = ans % 1000000007

	fmt.Printf("%d\n", ans)
}