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 pow(x,n)
  if n == 0
    1
  elsif n % 2 == 0
    pow(x*x%MOD, n/2) % MOD
  else
    x * pow(x, n-1) % MOD
  end
end

n = gets.to_i
dp = Array.new(n+1){Array.new(3,0)}
dp[0][0] = 1
if n == 1
  puts 0
else
  n.times do |i|
    dp[i+1][0] = (dp[i][0] * 8) % MOD
    dp[i+1][1] = (dp[i][0] * 2 + dp[i][1] * 9) % MOD
    dp[i+1][2] = (dp[i][1] * 1 + dp[i][2] * 10) % MOD
  end
  puts dp[n][2]
end