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)

n = int(input())
if n == 1:
    print(0)
    exit()
ans1 = 1
ans2 = 1
ans3 = 1
for i in range(n):
    ans1 = (ans1*10)%1000000007
    ans2 = (ans2*9)%1000000007
    ans3 = (ans3*8)%1000000007

ans = (ans1 - ans2*2 + ans3)%1000000007

print(ans)