<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 dx[8] = {2,2,1,1,-2,-2,-1,-1};
int dy[8] = {1,-1,2,-2,1,-1,2,-2};

int f(int n,int row,int column,vector<vector<vector<int>>>&dp){
 if(row<0 || column<0 || row>3 || column>2 || (row==3 && column==0) || (row==3 && column==2)) return 0;
        if(n==1) return 1; //if moves are exhausted (CATCH OF THE PROBLEM)
        if(dp[n][row][column]!=-1) return dp[n][row][column];
        int x_dir[8] = {-2,-2,-1,-1,+1,+1,+2,+2};
        int y_dir[8] = {-1,+1,-2,+2,-2,+2,-1,+1};
        long long ans=0;
        for(int k=0;k<8;k++){
            int x_val = x_dir[k];
            int y_val = y_dir[k];
            ans += f(n-1,row+x_val,column+y_val,dp)%MOD;
        }
        return dp[n][row][column] = ans%MOD;
    
}
    int knightDialer(int n) {
        vector<vector<vector<int>>>dp(n+1,vector<vector<int>>(4,vector<int>(3,-1)));
        int val=0;
        for(int i=0;i<4;i++){
            for(int j=0;j<3;j++){
                if(!(i==3 && j==0) && !(i==3 && j==2)){
                    val= val%MOD + f(n,i,j,dp)%MOD;
                }
            }
        }
        return (val%MOD);
    }
};
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