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Contest: Task: Related: TaskB TaskD

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