<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:
    bool isValid(int x,int y){
        if(x>=0 && x<4 && y>=0 && y<3) return 1;
        return 0;
    }
    long long int helper(int x,int y,int n,vector<vector<int>>&matrix, vector<vector<vector<long long int>>>&dp, vector<vector<int>>&directions){
        // base case

        if(n==0) return 1;
        if(dp[x][y][n]!=-1) return dp[x][y][n];

        long long int ways  =0;
        long long int mod  = 1e9+7;

        for(int i=0;i<8;i++){
            int newx = x+ directions[i][0];
            int newy = y+ directions[i][1];
            if(isValid(newx,newy) && matrix[newx][newy]!=-1){
                ways = ((ways%mod)+(helper(newx,newy,n-1,matrix,dp,directions))%mod)%mod;
            }
        }

        return dp[x][y][n] = ways%mod;
    }
    int knightDialer(int n) {
        vector<vector<int>> matrix;
        matrix.push_back({1,2,3});
        matrix.push_back({4,5,6});
        matrix.push_back({7,8,9});
        matrix.push_back({-1,0,-1});

        vector<vector<int>> directions = {{-2,-1},{-2,1},{-1,2},{1,2},{2,1},{2,-1},{1,-2},{-1,-2}};
        vector<vector<vector<long long int>>>dp(4,vector<vector<long long int>>(3,vector<long long int>(n,-1)));

        long long int ans  =0;
        long long int mod  = 1e9 +7;

        for(int i=0;i<4;i++){
            for(int j=0;j<3;j++){
                if(matrix[i][j]!=-1){
                    // vector<vector<vector<int>>>dp(4,vector<vector<int>>(3,vector<int>(n,-1)));
                    ans  = ((ans%mod)+(helper(i,j,n-1,matrix,dp,directions))%mod)%mod;
                    
                }
            }
        }

        return ans;
        
    }
};
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