Ubiquity

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

inputFormat

outputFormat

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

样例

869121

2511445