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())


def add(a, b, BIGMOD):
    return (a + b) % BIGMOD


def sub(a, b, BIGMOD):
    return (a - b + BIGMOD) % BIGMOD


MOD = 10 ** 9 + 7

D = pow(10, N, MOD)
C = pow(8, N, MOD)
A = pow(9, N, MOD)
B = A

print(sub(D,sub(add(A,B,MOD),C,MOD),MOD))