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"
	"math"
	"os"
	"strconv"
)

var mod = math.Pow10(9) + 7

func main() {
	sc := bufio.NewScanner(os.Stdin)
	sc.Scan()
	n, _ := strconv.Atoi(sc.Text())

	u := Pow(10, n, mod)

	a := Pow(9, n, mod)
	b := Pow(9, n, mod)
	c := Pow(8, n, mod)

	ans := u - a - b + c
	ans = math.Mod(ans, mod)
	ans = math.Mod(ans+mod, mod)

	fmt.Println(int(ans))
}

func Pow(x, y int, mod float64) float64 {
	var ans = float64(1)
	for i := 0; i < y; i++ {
		ans = math.Mod(ans*float64(x), mod)
	}
	return ans
}