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.

Input

Input is given from Standard Input in the following format:
N

Output

Print the answer modulo 10^9 + 7.

Constraints

• $1 \leq N \leq 10^6$
• N is an integer.

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

见题面 Input 部分

见题面 Output 部分