<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=1e9+7;
    int dr[8]={2,-2,2,-2,-1,-1,1,1};
    int dc[8]={1,1,-1,-1,2,-2,2,-2};
    long long help(int i,int j,int k,vector<vector<int>>&matrix,vector<vector<vector<long long>>>&dp){
            if(i>3||j>2||i<0||j<0||matrix[i][j]==-1)
            return 0;
            if(k==0)
            return 1;
            if(dp[i][j][k]!=-1)
            return dp[i][j][k];
            int ans=0;
            for(int l=0;l<8;l++){
                int nr=i+dr[l];
                int nc=j+dc[l];
                ans=(ans+help(nr,nc,k-1,matrix,dp))%mod;

            }
            return dp[i][j][k]=ans;
    }
    int knightDialer(int n) {
        long long ans=0;
        int p=1;
        vector<vector<int>>matrix(4,vector<int>(3,-1));
        for(int i=0;i<3;i++){
            for(int j=0;j<3;j++){
                matrix[i][j]=p;
                p++;
            }
        }
        matrix[3][1]=0;
        vector<vector<vector<long long>>>dp(5,vector<vector<long long>>(4,vector<long long>(n+1,-1)));
        for(int i=0;i<4;i++){
            for(int j=0;j<3;j++){
                if(matrix[i][j]!=-1){
                  ans=(ans+help(i,j,n-1,matrix,dp))%mod;
                }
            }
        }
        return ans;
    }
};
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