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 int64
	const M int64 = 1000000007
	fmt.Scanf("%d", &N)

	// 10^N
	var A int64 = 10
	var i int64 = 0
	for i = 1; i < N; i++ {
		A = A * 10 % M
	}

	var B int64 = 9
	for i = 1; i < N; i++ {
		B = B * 9 % M
	}

	var C int64 = 8
	for i = 1; i < N; i++ {
		C = C * 8 % M
	}

	B = (B + B) % M
	B = (B - C) % M

	A = (A - B) % M
	A %= M
	//A = (A / M) % M
	fmt.Printf("%d\n", A)
	// 10^N - (9^N + 9^N - 8^N)
	// 100 - (81 + 81 - 64)
	// 100 - (162-64) = 2

}