<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 {
private:
    int mod = 1e9+7;
    vector<vector<int>> arr;
    vector<vector<vector<int>>> dp;
    vector<int> x = {-1,1,-2,-2,-1,1,2,2};  //moves in row
    vector<int> y = {-2,-2,-1,1,2,2,-1,1};  //corresponding move in col
    int dialUtil(int moves, int row, int col)
    {
        // cout<<moves<<" "<<row<<" "<<col<<endl;
        if(arr[row][col] == -1) return 0;
        if(moves == 0) {
            // cout<<"affirmitive"<<endl;
            return 1;
        }
        
        if(dp[moves][row][col]!=-1) return dp[moves][row][col];
        int ans = 0;

        for(int k = 0;k<8;k++)
        {
            int rtemp = row+x[k];
            int ctemp = col+y[k];
            if(rtemp >=4 || ctemp>=3 || rtemp<0||ctemp<0||moves<=0) continue;
            ans = (ans+dialUtil(moves-1, rtemp, ctemp))%mod;
        }
    
            
        
        dp[moves][row][col] = ans;
        return ans;
    }
public:
    int knightDialer(int n) {
        int cnt = 1;
        // vector<vector<int>> arr(4, vector<int>(3,-1));
        arr.resize(5, vector<int>(4, -1)); // All elements initialized to -1
        dp.resize(n+1, vector<vector<int>>(5, vector<int>(4, -1))); 
        for(int i = 0;i<3;i++)
        {
            for(int j = 0;j<3;j++)
            {
                arr[i][j] = cnt;
                cnt++;
            }
        }
        arr[3][1] = 0;
        int ans = 0;
        for(int i = 0;i<4;i++)
        {
            for(int j = 0;j<3;j++)
            {
                if(arr[i][j]!=-1)
                    ans = (ans + dialUtil(n-1,i,j))%mod;
            }
        }
        return ans;
    }
};
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