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"
)

const mod = 1000000007

func main() {
	var n int
	fmt.Scan(&n)

	ans := (powmod(10, n) - 2*powmod(9, n) + powmod(8, n)) % mod
	fmt.Println(ans)
}

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