<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 m = 1e9+7 ;
    int dp[10][5005] ;
    int solve(int idx , map<int,vector<int>>& mp ,int n){
        
        if(n == 1){
            return 1 ;
        }

        if(dp[idx][n] != -1){
            return dp[idx][n] ;
        }

        vector<int> v = mp[idx] ;
        long long ans = 0 ;

        for(auto it : v){
            ans = ans + solve(it , mp , n-1)%m  ;
            ans = ans %m ;
        }

        return dp[idx][n] = ans%m ;

    }
    int knightDialer(int n) {
        
        // i am store that (intial at , where we move) ;

        map<int,vector<int>> mp ; 

        mp[0] = {4,6} ;
        mp[1] = {6,8} ;
        mp[2] = {7,9} ;
        mp[3] = {4,8} ;
        mp[4] = {3,9,0} ;
        mp[5] = {} ;
        
        mp[6] = {1,7,0} ;
        mp[7] = {2,6} ;
        
        mp[8] = {1,3} ;
        mp[9] = {2,4} ;

        long long ans = 0 ;
        memset(dp , -1 , sizeof(dp)) ;

        for(int i =0 ;i<=9 ;i++){
           ans = ans + solve(i , mp , n)%m ;
           ans = ans % m ;
        }
       
        
        return ans ;

    }
};
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