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)

import math
N = int(input())

MOD_VALUE = math.pow(10, 9) + 7

def pow_mod(value, pow):
    ret = 1
    for _ in range(pow):
        ret = ret * value % MOD_VALUE
    return ret

result = pow_mod(10, N) - pow_mod(9, N) * 2 + pow_mod(8, N)

print(int(result % MOD_VALUE))