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 PyPy3 (7.3.0) (judge verdict: Accepted)

N = int(input())
TEN = 1
NINE = 1
EIGHT = 1
a = 10
b = 9
c = 8

mod = 10 ** 9 + 7

for i in range(64):
    if N % 2:
        TEN *= a
        TEN %= mod
        NINE *= b
        NINE %= mod
        EIGHT *= c
        EIGHT %= mod
    N //= 2
    a *= a
    a %= mod
    b *= b
    b %= mod
    c *= c
    c %= mod

print((TEN - 2 * NINE + EIGHT + mod * 2)%mod)