<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:
    int mod = 1000000007;
    int knightDialer(int n) {
        if(n==1) return 10;
        vector<vector<int>> mat = {
            {4, 6},    // Moves from 0
            {6, 8},    // Moves from 1
            {7, 9},    // Moves from 2
            {4, 8},    // Moves from 3
            {0, 3, 9}, // Moves from 4
            {},        // 5 has no valid moves (center of the keypad)
            {0, 1, 7}, // Moves from 6
            {2, 6},    // Moves from 7
            {1, 3},    // Moves from 8
            {2, 4}     // Moves from 9
        };

        vector<int> dp(10,0);
        dp[0]=2;
        dp[1]=2;
        dp[2]=2;
        dp[3]=2;
        dp[4]=3;
        dp[5]=0;
        dp[6]=3;
        dp[7]=2;
        dp[8]=2;
        dp[9]=2;

        for(int i=3;i<=n;i++){
            vector<int> curr(10,0);
            for(int j=0;j<10;j++){
                int count = 0;
                for(int k=0;k<mat[j].size();k++){
                    count =( count +dp[mat[j][k]])%mod;
                }
                curr[j]=count%mod;
               
            }

            dp=curr;
        }
        int sum = 0;
        for(int i=0;i<10;i++){
            sum=(sum+dp[i])%mod;
        }

        return sum%mod;
    }
};
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