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
n = gets.to_i
ans1 = 1
ans2 = 1
ans3 = 1
n.times do
  ans1 = ans1 * 10 % MOD
  ans2 = ans2 * 9 % MOD
  ans3 = ans3 * 8 % MOD
end
puts (ans1 - ans2 * 2 + ans3 + MOD) % MOD