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())

def modpow(a, n, mod):
  res = 1
  while n > 0:
    if n & 1:
      res = res * a % mod
    a = a * a % mod
    n >>= 1
  return res

mod = 1000000007
ans = modpow(10, n, mod) - (modpow(9, n, mod) + modpow(9, n, mod) - modpow(8, n, mod))
ans = ans % mod
print(ans)