# ---
# title: 935. Knight Dialer
# id: problem935
# author: Tian Jun
# date: 2020-10-31
# difficulty: Medium
# categories: Dynamic Programming
# link: <https://leetcode.com/problems/knight-dialer/description/>
# hidden: true
# ---
# 
# The chess knight has a **unique movement** , it may move two squares
# vertically and one square horizontally, or two squares horizontally and one
# square vertically (with both forming the shape of an **L** ). The possible
# movements of chess knight are shown in this diagaram:
# 
# A chess knight can move as indicated in the chess diagram below:
# 
# ![](https://assets.leetcode.com/uploads/2020/08/18/chess.jpg)
# 
# We have a chess knight and a phone pad as shown below, the knight **can only
# stand on a numeric cell**  (i.e. blue cell).
# 
# ![](https://assets.leetcode.com/uploads/2020/08/18/phone.jpg)
# 
# Given an integer `n`, return how many distinct phone numbers of length `n` we
# can dial.
# 
# You are allowed to place the knight **on any numeric cell** initially and then
# you should perform `n - 1` jumps to dial a number of length `n`. All jumps
# should be **valid** knight jumps.
# 
# As the answer may be very large, **return the answer modulo** `109 + 7`.
# 
# 
# 
# **Example 1:**
# 
#     
#     
#     Input: n = 1
#     Output: 10
#     Explanation: We need to dial a number of length 1, so placing the knight over any numeric cell of the 10 cells is sufficient.
#     
# 
# **Example 2:**
# 
#     
#     
#     Input: n = 2
#     Output: 20
#     Explanation: All the valid number we can dial are [04, 06, 16, 18, 27, 29, 34, 38, 40, 43, 49, 60, 61, 67, 72, 76, 81, 83, 92, 94]
#     
# 
# **Example 3:**
# 
#     
#     
#     Input: n = 3
#     Output: 46
#     
# 
# **Example 4:**
# 
#     
#     
#     Input: n = 4
#     Output: 104
#     
# 
# **Example 5:**
# 
#     
#     
#     Input: n = 3131
#     Output: 136006598
#     Explanation: Please take care of the mod.
#     
# 
# 
# 
# **Constraints:**
# 
#   * `1 <= n <= 5000`
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
