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 Julia (1.4.0) (judge verdict: Wrong Answer)

function main()
  n=parse(Int,readline())
  a,b,c=1,1,1
  d=1e9+7
  for i=1:n
    a=mod(10*a,d)
    b=mod(9*b,d)
    c=mod(8*c,d)
  end
  println(mod((a-2b+c),d))
end
main()