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 PyPy3 (7.3.0) (judge verdict: Accepted)

def modexp(a,b,mod):
    if b==0:
        return 1
    elif b%2==0:
        x=modexp(a%mod,b//2,mod)%mod
        return (x*x)%mod
    else:
        return ((a%mod)*(modexp(a%mod,b-1,mod)%mod))

mod=10**9+7
n=int(input())
a=modexp(10,n,mod)
b=modexp(9,n,mod)
c=modexp(8,n,mod)
ans=((a+c)%mod)-((2*b)%mod)
print(ans%mod)