<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 r=4,c=3,mod=1e9+7;
    vector<vector<int>> v;
    vector<int> xv = {2, 2, -2, -2, 1, 1, -1, -1};
    vector<int> yv = {1, -1, 1, -1, 2, -2, 2, -2};
    int dp[5][5][50001];

    bool isvalid(int i, int j){
        if(i>=0 && i<r && j>=0 && j<c && v[i][j]!=-2) return 1;
        return 0;
    }
    
    int util(int x, int y, int cnt, int n){
        if(cnt==n) return 1; 

        if(dp[x][y][cnt]!=-1) return dp[x][y][cnt];

        int ans=0;
        for(int k=0; k<8; k++){
            if(isvalid(x+xv[k],y+yv[k])){
            ans=(ans%mod+util(x+xv[k],y+yv[k],cnt+1,n)%mod)%mod;
            }
        }
    

        return dp[x][y][cnt]=ans;
    }

    int knightDialer(int n) {
        int out=0;
        v={{1,2,3},{4,5,6},{7,8,9},{-2,0,-2}};
        memset(dp,-1,sizeof(dp));

        for(int i=0; i<r; i++){
            for(int j=0; j<c; j++){
                if(v[i][j]!=-2)
                out=(out+util(i,j,1,n))%mod;
            }
        }

        return out;
    }
};
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