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 Python (3.8.2) (judge verdict: Accepted)

N=int(input())
MOD=10**9+7
MAX=N+1
def powermod(base,ind):
  if ind==1:
    return base
  elif ind%2==0:
    return (powermod(base,ind//2)**2)%MOD
  else:
    return ((powermod(base,ind//2)**2)*base)%MOD

print((powermod(10,N)-2*powermod(9,N)+powermod(8,N))%MOD)