p02554 AtCoder Beginner Contest 178 - 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
```python
N = int(input())

ans = 10**N - 2*(9**N) + 8**N
print(ans % 1000000007)

```