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 Python (3.8.2) (judge verdict: Accepted)

def main():
	N = int(input())
	p = 1000000007
	ten = [10]
	nine = [9]
	eight = [8]
	for i in range(23):
		ten.append((ten[-1] ** 2) % p)
		nine.append((nine[-1] ** 2) % p)
		eight.append((eight[-1] ** 2) % p)

	t = 1
	n = 1
	e = 1

	b_N = format(N, 'b')
	for i in range(len(b_N)):
		if b_N[- 1 - i] == "1":
			t = (t * ten[i]) % p
			n = (n * nine[i]) % p
			e = (e * eight[i]) % p
	print((t - 2 * n + e) % p)

main()