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: Accepted)

const m=1000000007
function main()
    n=myread(Int)
    println(mod(powermod(10,n,m)-2*powermod(9,n,m)+powermod(8,n,m),m))
end

# ----------input function----------
sread()=chomp(readline())
sreads(sp=" ")=split(readline(),sp)
myread(ty)=parse(ty,readline())
myreads(ty)=map(x->parse(ty,x),split(readline()))
main()