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: Wrong Answer)

S = 10 ** 9 + 7

def mpow(n, p, mod)
  r = 1
  while p > 0
    r = r * n % mod if p % 2 == 1
    n = n * n % mod
    p >>= 1
  end
  r
end

N = gets.to_i
# 8

if N == 1 then
  puts 0
elsif N == 2 then
  puts 2
else
  c = 0
  n = N * (N - 1) % S
  (2..N).each do |i|
    tp = mpow(8, N - i, S)
    c += n * tp
    c %= S

    n *= (2 * (N - i)) % S
    n %= S
  end
  puts c
end