<p>You are given a <code>rows x cols</code> matrix <code>grid</code> representing a field of cherries where <code>grid[i][j]</code> represents the number of cherries that you can collect from the <code>(i, j)</code> cell.</p>

<p>You have two robots that can collect cherries for you:</p>

<ul>
	<li><strong>Robot #1</strong> is located at the <strong>top-left corner</strong> <code>(0, 0)</code>, and</li>
	<li><strong>Robot #2</strong> is located at the <strong>top-right corner</strong> <code>(0, cols - 1)</code>.</li>
</ul>

<p>Return <em>the maximum number of cherries collection using both robots by following the rules below</em>:</p>

<ul>
	<li>From a cell <code>(i, j)</code>, robots can move to cell <code>(i + 1, j - 1)</code>, <code>(i + 1, j)</code>, or <code>(i + 1, j + 1)</code>.</li>
	<li>When any robot passes through a cell, It picks up all cherries, and the cell becomes an empty cell.</li>
	<li>When both robots stay in the same cell, only one takes the cherries.</li>
	<li>Both robots cannot move outside of the grid at any moment.</li>
	<li>Both robots should reach the bottom row in <code>grid</code>.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/04/29/sample_1_1802.png" style="width: 374px; height: 501px;" />
<pre>
<strong>Input:</strong> grid = [[3,1,1],[2,5,1],[1,5,5],[2,1,1]]
<strong>Output:</strong> 24
<strong>Explanation:</strong> Path of robot #1 and #2 are described in color green and blue respectively.
Cherries taken by Robot #1, (3 + 2 + 5 + 2) = 12.
Cherries taken by Robot #2, (1 + 5 + 5 + 1) = 12.
Total of cherries: 12 + 12 = 24.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/04/23/sample_2_1802.png" style="width: 500px; height: 452px;" />
<pre>
<strong>Input:</strong> grid = [[1,0,0,0,0,0,1],[2,0,0,0,0,3,0],[2,0,9,0,0,0,0],[0,3,0,5,4,0,0],[1,0,2,3,0,0,6]]
<strong>Output:</strong> 28
<strong>Explanation:</strong> Path of robot #1 and #2 are described in color green and blue respectively.
Cherries taken by Robot #1, (1 + 9 + 5 + 2) = 17.
Cherries taken by Robot #2, (1 + 3 + 4 + 3) = 11.
Total of cherries: 17 + 11 = 28.
</pre>

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

<ul>
	<li><code>rows == grid.length</code></li>
	<li><code>cols == grid[i].length</code></li>
	<li><code>2 &lt;= rows, cols &lt;= 70</code></li>
	<li><code>0 &lt;= grid[i][j] &lt;= 100</code></li>
</ul>

class Solution {
public:

    vector<vector<int>> grid;

    bool isValid(int x, int y)
    {
        if(x<0 || y<0 || x>=grid.size() || y>=grid[0].size())
            return false;
        return true;
    }

    bool isValid(int x1, int y1, int x2, int y2)
    {
        return isValid(x1, y1) && isValid(x2, y2);
    }

    int dp[71][71][71];
    bool validdp[71][71][71];

    int findBest(int x1, int y1, int x2, int y2)
    {
        // assert(x1==x2);
        // assert(isValid(x1, y1, x2, y2));
        if(validdp[x1][y1][y2])
            return dp[x1][y1][y2];
        if(x1==grid.size()-1)
            return 0;
        int best = 0;

        for(int i=-1; i<=1; i++)
            for(int j=-1; j<=1; j++)
            {
                int nx1 = x1+1;
                int nx2 = x2+1;
                int ny1 = y1+i;
                int ny2 = y2+j;
                if(!isValid(nx1, ny1, nx2, ny2))
                    continue;
                int ans = grid[nx1][ny1];
                if(nx2!=nx1 || ny2!=ny1)
                    ans += grid[nx2][ny2];     
                ans += findBest(nx1, ny1, nx2, ny2);
                best = max(best, ans);
            }

        validdp[x1][y1][y2] = true;
        dp[x1][y1][y2] = best;
        return best;
    }

    int cherryPickup(vector<vector<int>>& grid) 
    {
        memset(validdp, 0, sizeof(validdp));
        this->grid = grid;
        int x1 = 0, y1 = 0;
        int x2 = 0, y2 = grid[0].size()-1;
        return findBest(x1, y1, x2, y2) + grid[x1][y1] + grid[x2][y2];
    }
};
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