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)

def modpow(a, n, m)
  return 1 if n == 0

  tmp = modpow(a, n / 2, m)
  n % 2 == 0 ? tmp * tmp % m : tmp * tmp * a % m
end

n = gets.chomp.to_i
M = (1e9+7).to_i
puts (modpow(10, n, M) - 2 * modpow(9, n, M) + modpow(8, n, M)) % M