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)

n=int(input())
mod=10**9+7

dp=[[0,0,0,0] for _ in range(n)]

dp[0]=[8,1,1,0]

for i in range(1,n):
    dp[i][0]=(dp[i-1][0]*8)%mod
    dp[i][1]=(dp[i-1][0]+dp[i-1][1]*9)%mod
    dp[i][2]=(dp[i-1][0]+dp[i-1][2]*9)%mod
    dp[i][3]=(dp[i-1][1]+dp[i-1][2]+dp[i-1][3]*10)%mod

#print(dp)

print(dp[-1][3]%mod)