<p>The chess knight has a <strong>unique movement</strong>,&nbsp;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 <strong>L</strong>). The possible movements of chess knight are shown in this diagram:</p>

<p>A chess knight can move as indicated in the chess diagram below:</p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/08/18/chess.jpg" style="width: 402px; height: 402px;" />
<p>We have a chess knight and a phone pad as shown below, the knight <strong>can only stand on a numeric cell</strong>&nbsp;(i.e. blue cell).</p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/08/18/phone.jpg" style="width: 242px; height: 322px;" />
<p>Given an integer <code>n</code>, return how many distinct phone numbers of length <code>n</code> we can dial.</p>

<p>You are allowed to place the knight <strong>on any numeric cell</strong> initially and then you should perform <code>n - 1</code> jumps to dial a number of length <code>n</code>. All jumps should be <strong>valid</strong> knight jumps.</p>

<p>As the answer may be very large, <strong>return the answer modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> 10
<strong>Explanation:</strong> We need to dial a number of length 1, so placing the knight over any numeric cell of the 10 cells is sufficient.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 2
<strong>Output:</strong> 20
<strong>Explanation:</strong> 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]
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> n = 3131
<strong>Output:</strong> 136006598
<strong>Explanation:</strong> Please take care of the mod.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 5000</code></li>
</ul>

class Solution {
public:
    vector<vector<int>> neighbors = {{4, 6}, {6, 8}, {7, 9}, {4, 8}, {3, 9, 0}, {}, {1, 7, 0}, {2, 6}, {1, 3}, {2, 4}};
    int knightDialer(int n) {
        // 1 - 6, 8
        // 2 - 7, 9
        // 3 - 4, 8
        // 4 - 3, 9, 0
        // 5 - 
        // 6 - 1, 7, 0
        // 7 - 2, 6
        // 8 - 1, 3
        // 9 - 2, 4
        // 0 - 4, 6

        vector<vector<int>> dp (10, vector<int> (n));
        for (int i = 0; i <= 9; i++) {
            dp[i][0] = 1;
        }

        for (int j = 1; j < n; j++) {
            for (int i = 0; i <= 9; i++) {
                auto dests = neighbors[i];
                int sum = 0;
                for (auto& d : dests) {
                    sum += dp[d][j-1];
                    sum %= 1000000007;
                }
                dp[i][j] = sum % 1000000007;
            }
        }

        int res = 0;
        for (int i = 0; i <= 9; i++) {
            res += dp[i][n-1];
            res %= 1000000007;
        }

        return res;
    }
};
130187