<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:
    def cherryPickup(self, grid: List[List[int]]) -> int:
        # def fn(i, j1, j2):
        #     if i<0 or i>=r or j1<0 or j1>=c or j2<0 or j2>=c:
        #         return float('-inf')
        #     if i==r-1:
        #         if j1==j2:
        #             return grid[i][j1]
        #         else:
        #             return grid[i][j1] + grid[i][j2]
        #     if (i,j1, j2) in cache:
        #         return cache[(i, j1, j2)]
        #     else:
        #         if j1==j2:
        #             val = grid[i][j1]        
        #         else:
        #             val = grid[i][j1] + grid[i][j2]

        #         maxVal = float('-inf')
        #         for dj1 in range(-1, 2):
        #             for dj2 in range(-1, 2):        
        #                 maxVal = max(maxVal, fn(i+1, j1+dj1, j2+dj2))
        #         cache[(i, j1, j2)] = val+maxVal    
        #         return cache[(i, j1, j2)]

        r = len(grid)
        c = len(grid[0])
        dp = [[[float('-inf') for _ in range(c)] for j in range(c)] for i in range(r)]
        for j1 in range(c):
            for j2 in range(c):
                if j1==j2:
                    dp[r-1][j1][j2] = grid[r-1][j1]
                else:
                    dp[r-1][j1][j2] = grid[r-1][j1] + grid[r-1][j2]
        
        for i in range(r-2, -1, -1):
            for j1 in range(c):
                for j2 in range(c):
                    if j1==j2:
                        val = grid[i][j1]
                    else:
                        val = grid[i][j1] + grid[i][j2]
                    maxVal = float('-inf')
                    for dj1 in range(-1, 2):
                        for dj2 in range(-1, 2):
                            if 0<=j1+dj1<c and 0<=j2+dj2<c:        
                                maxVal = max(maxVal, dp[i+1][j1+dj1][j2+dj2])
                    dp[i][j1][j2] = val + maxVal

        return dp[0][0][c-1]
29683