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 = 1_000_000_007
n = gets.to_i

dp = Array.new(n + 1) { Array.new(2) { Array.new(2, 0) }}
dp[0][0][0] = 1

n.times do |i|
  dp[i+1][0][0] = (dp[i][0][0] * 8) % MOD
  dp[i+1][0][1] = (dp[i][0][0] + dp[i][0][1] * 9) % MOD
  dp[i+1][1][0] = (dp[i][0][0] + dp[i][1][0] * 9) % MOD
  dp[i+1][1][1] = (dp[i][1][0] + dp[i][0][1] + dp[i][1][1] * 10) % MOD
end

p dp[n][1][1]