<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:
    bool is_valid(int r, int c, int N, int M) {
        return (0 <= r && r < N) && (0 <= c && c < M);
    }
    bool is_same(int r1, int c1, int r2, int c2) {
        return r1 == r2 && c1 == c2;
    }
    int dp[73][73][73];
    int solve(int row1, int col1, int row2, int col2, vector<vector<int>>& g) {
        const int N = g.size();
        const int M = g[0].size();
        if (row1 == N) {
            return 0;
        }
        if (dp[row1][col1][col2] != -1) {
            return dp[row1][col1][col2];
        }
        const vector<int> dirs({-1, 0, 1});
        int ans = 0;
        for (auto& direction1 : dirs) {
            for (auto& direction2 : dirs) {
                int R1 = row1 + 1;
                int C1 = col1 + direction1;
                int R2 = row2 + 1;
                int C2 = col2 + direction2;

                if (is_valid(R1, C1, N, M) && is_valid(R2, C2, N, M)) {

                    ans = max(ans, is_same(R1, C1, R2, C2)
                                       ? g[R1][C1]
                                       : g[R1][C1] + g[R2][C2] +
                                             solve(R1, C1, R2, C2, g));
                }
            }
        }

        return dp[row1][col1][col2] =  ans;
    }
    int cherryPickup(vector<vector<int>>& grid) {
        const int N = grid.size();
        const int M = grid[0].size();
        for (int i = 0 ; i  < N ; i += 1)
            for (int j = 0 ; j < M ; j += 1)
                    for (int j1 = 0 ; j1 < M ; j1 += 1)
                        dp[i][j][j1] = -1;
        return grid[0][0] + grid[0][M - 1] + solve(0, 0, 0, M - 1, grid);
    }
};
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