<p>You are given an <code>n x n</code> <code>grid</code> representing a field of cherries, each cell is one of three possible integers.</p>

<ul>
	<li><code>0</code> means the cell is empty, so you can pass through,</li>
	<li><code>1</code> means the cell contains a cherry that you can pick up and pass through, or</li>
	<li><code>-1</code> means the cell contains a thorn that blocks your way.</li>
</ul>

<p>Return <em>the maximum number of cherries you can collect by following the rules below</em>:</p>

<ul>
	<li>Starting at the position <code>(0, 0)</code> and reaching <code>(n - 1, n - 1)</code> by moving right or down through valid path cells (cells with value <code>0</code> or <code>1</code>).</li>
	<li>After reaching <code>(n - 1, n - 1)</code>, returning to <code>(0, 0)</code> by moving left or up through valid path cells.</li>
	<li>When passing through a path cell containing a cherry, you pick it up, and the cell becomes an empty cell <code>0</code>.</li>
	<li>If there is no valid path between <code>(0, 0)</code> and <code>(n - 1, n - 1)</code>, then no cherries can be collected.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/12/14/grid.jpg" style="width: 242px; height: 242px;" />
<pre>
<strong>Input:</strong> grid = [[0,1,-1],[1,0,-1],[1,1,1]]
<strong>Output:</strong> 5
<strong>Explanation:</strong> The player started at (0, 0) and went down, down, right right to reach (2, 2).
4 cherries were picked up during this single trip, and the matrix becomes [[0,1,-1],[0,0,-1],[0,0,0]].
Then, the player went left, up, up, left to return home, picking up one more cherry.
The total number of cherries picked up is 5, and this is the maximum possible.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> grid = [[1,1,-1],[1,-1,1],[-1,1,1]]
<strong>Output:</strong> 0
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= n &lt;= 50</code></li>
	<li><code>grid[i][j]</code> is <code>-1</code>, <code>0</code>, or <code>1</code>.</li>
	<li><code>grid[0][0] != -1</code></li>
	<li><code>grid[n - 1][n - 1] != -1</code></li>
</ul>

class Solution {
public:
    int solve(vector<vector<int>>& grid, vector<vector<vector<int>>> &dp, int r1, int c1, int r2){
        int n = grid.size();
        int c2 = r1+c1-r2;
        if(r1<0 || r2<0 || c1<0 || c2<0 || r1==n || r2==n || c1==n || c2==n || grid[r1][c1]==-1 || grid[r2][c2]==-1){
            return -1e8;
        }

        if(dp[r1][c1][r2]!=-1){
            return dp[r1][c1][r2];
        }

        vector<pair<int, int>> drns = {{-1, 0}, {0, -1}};
        int cherries = grid[r1][c1] + grid[r2][c2];

        if(r1==r2 && c1==c2){
            cherries = grid[r1][c1];
        }

        int maxi = -1e8;

        maxi = max(maxi, solve(grid, dp, r1, c1-1, r2));
        maxi = max(maxi, solve(grid, dp, r1-1, c1, r2));
        maxi = max(maxi, solve(grid, dp, r1, c1-1, r2-1));
        maxi = max(maxi, solve(grid, dp, r1-1, c1, r2-1));

        if(maxi==-1e8){
            return dp[r1][c1][r2] = maxi;
        }

        return dp[r1][c1][r2] = maxi + cherries;

    }

    int cherryPickup(vector<vector<int>>& grid) {
        int n = grid.size();

        vector<vector<vector<int>>> dp(n, vector<vector<int>>(n, vector<int>(n, -1)));
        dp[0][0][0] = (grid[0][0]!=-1) ? grid[0][0] : -1e8;
        dp[n-1][n-1][n-1] = solve(grid, dp, n-1, n-1, n-1);

        if(dp[n-1][n-1][n-1]<0){
            return 0;
        }

        return dp[n-1][n-1][n-1];
    }
};
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