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: Runtime Error)

from scipy.special import perm
n = int(input())
def re_factorial(n):
    if n < 2:
        return 1
    return n * re_factorial(n-1)
mas = n-2 # 0と9は必ず使う
#print(perm(n, 2))
if mas == 0:
  print(2)
elif n == 0:
  print(1)
else:
  #res = (permutations_count(n, 2) * 10^mas)%(10^9 + 7)
  res = (re_factorial(n)%1000000007 * int(perm(n, 2))%1000000007 * 10**mas%1000000007) %1000000007
  print(int(res))