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