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 (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

const modd int = 1000000007

func main() {
	scanInit()

	n := nextInt()

	ans := powMOD(10, n) - (powMOD(9, n) + powMOD(9, n) - powMOD(8, n))

	ans %= modd
	fmt.Println((ans + modd) % modd)

}
func powMOD(a, b int) int {
	var ret int = 1
	for b > 0 {
		if (b & 1) == 1 {
			ret *= a
			ret %= modd
		}
		a = a * a % modd
		b >>= 1
	}
	return ret
}

// ---- readfunc
var sc = bufio.NewScanner(os.Stdin)

func scanInit() {
	const cap = 200 * 1024 // default=64*1024
	var buf = make([]byte, cap)
	sc.Buffer(buf, cap)
	sc.Split(bufio.ScanWords)
	return
}
func nextInt() int {
	sc.Scan()
	i, _ := strconv.Atoi(sc.Text())
	return i
}
func nextStr() string {
	sc.Scan()
	return sc.Text()
}