Sequence h=1a+8b (h0=0,h1=1)
The sequence has h(0)=0, h(1)=1 and h(n)=1h(n−1)+8h(n−2). Print h(N) modulo 109+7.
Input: one integer N.
Output: h(N) mod 109+7.
Constraints:
- 0 ≤ N ≤ 1018
Sample Tests
Input 1
5
Output 1
89
Input 2
0
Output 2
0
Input 3
1
Output 3
1
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