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)

n = gets.to_i
t1 = 1 #0-9
t2 = 1 #1-8
t3 = 1 #1-9 or 0-8
mod = 10**9 + 7
for i in 0...n
  t1 *= 10
  t2 *= 8
  t3 *= 9
  t1 %= mod
  t2 %= mod
  t3 %= mod
end
ans = t1 - t2 - (t3-t2) * 2

ans %= mod

puts ans