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())
mod = 10**9+7

if(N == 1):
  count = 0
else:
  Pmax = 10**N #全組み合わせ数
  P0out = 9**N #0が入らない
  P9out  = 9**N #9が入らない
  P09out = 8**N #0も9も入らない
  
  count = Pmax - P09out - (P0out - P09out) - (P9out - P09out)
  
  
print(int(count%mod))