<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>> moves = {
        {4, 6},    // moves[0] = {4, 6}
        {6, 8},    // moves[1] = {6, 8}
        {7, 9},    // moves[2] = {7, 9}
        {4, 8},    // moves[3] = {4, 8}
        {0, 3, 9}, // moves[4] = {0, 3, 9}
        {},        // moves[5] = {}
        {0, 1, 7}, // moves[6] = {0, 1, 7}
        {2, 6},    // moves[7] = {2, 9}
        {1, 3},    // moves[8] = {1, 3}
        {2, 4}     // moves[9] = {2, 4}
    };
   

    const long long mod = 1e9 + 7;
    long long f(long long len, long long number, long long n,
                vector<vector<long long>>& dp) {
        if (len == n) {
            return 1;
        }
        if (number == 5) {
            return 0;
        }
        if (dp[len][number] != 0) {
            return dp[len][number];
        }
        long long res = 0;
        for (long long u : moves[number]) {
            res = (res+ f(len + 1, u, n, dp) ) %mod;
            res %= mod;
        }
        return dp[len][number] = res % mod;
    }

    long long knightDialer(long long n) {

        long long res = 0;
            vector<vector<long long>> dp(n + 1, vector<long long>(10, 0));
        for (long long i = 0; i < 10; i++) {
            res = (res + f(1, i, n, dp)) % mod;
        }
        return res;
    }
};
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