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 Ruby (2.7.1) (judge verdict: Accepted)

MOD = 10 ** 9 + 7
def powmod(n,r)
  return 1 if r.zero?
  return n if r == 1
  s = powmod(n, r / 2)
  return s * s % MOD if r.even?
  return n *  s * s % MOD
end
N = gets.to_i
ans = (powmod(10, N) - 2 * powmod(9, N) + powmod(8, N)) % MOD
puts ans