<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>

#define ll long long int 
class Solution {
public:
    ll N, M;
    ll arr[71][71][71];  // Uncomment and use this for memoization

    ll help(vector<vector<int>>& v, int i, int j,  int c) {
        int r =i;
        if (r < 0 || c < 0 || r >= N || c >= M || i < 0 || j < 0 || i >= N || j >= M)
            return -1e9;

        // Memoization check
        if (arr[i][j][c] != -1)
            return arr[i][j][c];
        
        if (r == N-1) { // last row
            if (i == N-1) {
                return (i == r && j == c) ? v[r][c] : v[r][c] + v[i][j];
            }
            return -1e9; // invalid since the two cannot end up on different rows
        }

        ll ch = 0;
        ll mx = -1e9, a, b, cc, d, e, f, g, h, ii;
        ch = ((i == r && j == c) ? v[r][c] : v[r][c] + v[i][j]);

        // Recursive calls
        a = help(v, i + 1, j - 1,  c - 1);
        b = help(v, i + 1, j - 1,  c);
        cc = help(v, i + 1, j - 1, c + 1);
        d = help(v, i + 1, j, c - 1);
        e = help(v, i + 1, j, c + 1);
        f = help(v, i + 1, j, c);
        g = help(v, i + 1, j + 1, c + 1);
        h = help(v, i + 1, j + 1,  c);
        ii = help(v, i + 1, j + 1, c - 1);
        
        mx = max({a, b, cc, d, e, f, g, h, ii});
        if (mx == -1e9) return arr[i][j][c] = -1e9;
        ch += mx;

        return arr[i][j][c] = ch; // Store in memoization table
    }

    int cherryPickup(vector<vector<int>>& grid) {
        N = grid.size();
        M = grid[0].size();
        memset(arr, -1, sizeof(arr));  // Initialize memoization table
        ll result = help(grid, 0, 0,  M - 1);
        return result <= -1e9 ? 0 : result;
    }
};

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