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)

MOD = 10 ** 9 + 7

n = int(input())

if n == 1:
    print(0)
    exit()

if n == 2:
    print(2)
    exit()

print((pow(10, n, MOD) - 2 * pow(9, n, MOD) + pow(8, n, MOD)) % MOD)

# 10 ^ n | 数列全体
#  9 ^ n | 0 を含まない数列全体
#  9 ^ n | 9 を含まない数列全体
#  8 ^ n | 0, 9 を含まない数列全体