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"
)

var sc = bufio.NewScanner(os.Stdin)
var out = bufio.NewWriter(os.Stdout)

func next() string {
	sc.Scan()
	return sc.Text()
}

func nextInt() int {
	a, _ := strconv.Atoi(next())
	return a
}

const DIV uint64 = 1e9 + 7

func pow(a uint64, n int) uint64 {
	if n == 0 {
		return 1
	} else if n%2 == 0 {
		p := pow(a, n/2)
		return p * p % DIV
	} else {
		p := pow(a, n/2)
		return a * p * p % DIV
	}
}

func main() {
	buf := make([]byte, 1024*1024)
	sc.Buffer(buf, bufio.MaxScanTokenSize)
	sc.Split(bufio.ScanWords)
	defer out.Flush()

	N := nextInt()
	ans := (2*DIV + pow(10, N) - 2*pow(9, N) + pow(8, N)) % DIV
	fmt.Fprintf(out, "%d\n", ans)
}