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"
	"math"
)

func main() {
	// Code for C - Ubiquity
	var N int
	fmt.Scan(&N)

	var a, b, c int
	var ans int
	a = 1
	b = 1
	c = 1
	for i := 0; i < N; i++ {
		a = (a * 10) % (int(math.Pow10(9)) + 7)
		b = (b * 9) % (int(math.Pow10(9)) + 7)
		c = (c * 8) % (int(math.Pow10(9)) + 7)
	}
	//fmt.Println(a, b, c)
	ans = (a - 2*b + c) % (int(math.Pow10(9)) + 7)
	fmt.Println(ans)
}