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.

Examples

Input

2

Output

2

Input

1

Output

0

Input

869121

Output

2511445

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