A chess knight can move as indicated in the chess diagram below:
This time, we place our chess knight on any numbered key of a phone pad (indicated above), and the knight makes N-1 hops. Each hop must be from one key to another numbered key.
Each time it lands on a key (including the initial placement of the knight), it presses the number of that key, pressing N digits total.
How many distinct numbers can you dial in this manner?
Since the answer may be large, output the answer modulo 10^9 + 7.
Example 1:
Input: 1
Output: 10
Example 2:
Input: 2
Output: 20
Example 3:
Input: 3
Output: 46
Note:
1 <= N <= 5000
1 2 3
4 5 6
7 8 9
* 0 #
4 可以到达 0， 4 -> 7 -> * -> 0。同理，6 也可以达到 0。