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())
mod = 10**9 + 7
contain_zero = 0
contain_nine = 0
not_contain_zero_and_nine = 0
all_per = pow(10,n,mod)
if n < 2:
    print(0)
else:
    contain_zero = all_per - pow(9,n,mod)
    contain_nine = all_per - pow(9,n,mod)
    not_contain_zero_and_nine = pow(8,n,mod)
    print((-(all_per - not_contain_zero_and_nine -contain_nine - contain_zero))%mod)