<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:

    long long move_in_board(vector<vector<vector<long long>>> &v, int n, int i, int j){

        
        if (i==3){
                    if (j==0 || j==2){
                        return 0;
                    }
                }
        
        if (i>=4 || j>=3 || i<0 || j<0){
            return 0;
        }
        if(n<=0){
            return 1;
        }
        // cout << i << j << n;
        if (v[i][j][n]!=-1){
            return v[i][j][n];
        }

        long long total_moves = 0;
        total_moves = (total_moves + move_in_board(v,n-1,  i+2, j+1) + move_in_board(v, n-1, i+2, j-1) + move_in_board(v, n-1, i+1, j+2) + move_in_board(v, n-1, i-1, j+2) + move_in_board(v,n-1,  i-2, j+1) + move_in_board(v, n-1, i-2, j-1) + move_in_board(v,n-1,  i+1, j-2) + move_in_board(v,n-1,  i-1, j-2))%(1000000007);

        v[i][j][n] = total_moves % (1000000007);
        return v[i][j][n] % (1000000007);


    }

    

    int knightDialer(int n) {
        vector<vector<vector<long long>>> v(4, vector<vector<long long>> (3, vector<long long> (n+1, -1)));
        long long ans = 0;
        cout << ans;

        for(int i=0;i<4;i++){
            for(int j=0; j<3;j++){
                // cout << move_in_board(v, n-1,i,j) << i << j << endl;
                ans = (ans +  move_in_board(v, n-1,i,j)) % 1000000007;

                
            }
        }

        return ans;




        
    }
};
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