<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 {

    int ROWS_COLS;
    int LAST_ROW_COL;
    vector<vector<vector<vector<int>>>> tab;

public:
    int maxRightDown (vector<vector<int>> &grid, int row1, int col1, int row2, int col2)
 {
   int res1 = 0;

   if (grid[row1][col1] == -1 || grid[row2][col2] == -1)
     return -1;
  
   if (tab[row1][col1][row2][col2] != -1)
     return tab[row1][col1][row2][col2];

    if (tab[row2][col2][row1][col1] != -1)
     return tab[row2][col2][row1][col1];

   if (row1 == LAST_ROW_COL && col1 == LAST_ROW_COL)
     return grid[row1][col1];
   else if (row2 == LAST_ROW_COL && col2 == LAST_ROW_COL)
      return grid[row2][col2];

   res1 = grid[row1][col1];
   if (row1 != row2 || col1 != col2)
    res1 += grid[row2][col2];

   int maxim = -1, max1 = -1, max2 = -1, max3 = -1, max4 = -1;
   if (row1 < LAST_ROW_COL && row2 < LAST_ROW_COL)
   {
        max1 = maxRightDown (grid, row1 + 1, col1, row2 + 1, col2);
        if (max1 > maxim)
            maxim = max1;
   }

   if (row1 < LAST_ROW_COL && col2 < LAST_ROW_COL)
   {
        max2 = maxRightDown (grid, row1 + 1, col1, row2, col2 + 1);
        if (max2 > maxim)
            maxim = max2;
   }
        
   if (col1 < LAST_ROW_COL && row2 < LAST_ROW_COL)
   {
        max3 = maxRightDown (grid, row1, col1 + 1, row2 + 1, col2);
        if (max3 > maxim)
            maxim = max3;
   }

   if (col1 < LAST_ROW_COL && col2 < LAST_ROW_COL)
   {
         max4 = maxRightDown (grid, row1, col1 + 1, row2, col2 + 1);
         if (max4 > maxim)
            maxim = max4;
   }
   
   if (maxim < 0)
     return tab[row1][col1][row2][col2] = INT_MIN;

   return tab[row1][col1][row2][col2] = res1 + maxim;
 }




 int cherryPickup(vector<vector<int>>& grid)
 {
    ROWS_COLS = grid.size();
    LAST_ROW_COL = ROWS_COLS - 1;
   vector<vector<vector<vector<int>>>> tab(ROWS_COLS, vector<vector<vector<int>>>(ROWS_COLS, 
    vector<vector<int>> (ROWS_COLS, vector<int>(ROWS_COLS, -1))));

 this->tab = std::move (tab);
 
  auto res = maxRightDown(grid, 0, 0, 0, 0);
  if (res < 0)
   return 0;
  return res;

 }

};
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