<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 {
public:
    int n;
    int m;
    bool isValid(vector<vector<int>> &grid, int i, int j){
        return i >= 0 && j >= 0 && i < n && j < m && grid[i][j] != -1; 
    }

    pair<int, bool> x(vector<vector<int>> &grid, int i1, int j1, int i2, int j2, unordered_map<string, pair<int, bool>> &dp){
        if(!isValid(grid, i1, j1) || !isValid(grid, i2, j2)){
            return {0, false};
        }
        
        string s = to_string(i1)+"."+to_string(j1)+"+"+to_string(i2)+"."+to_string(j2);
        if(i1 == n-1 && j1 == m-1){
            return {grid[i1][j1], true};
        }
        else if(dp.find(s) != dp.end()){
            return dp[s];
        }

        int curr = 0;
        if(i1 == i2 && j1 == j2){
            if(grid[i1][j1] == 1){
                curr++;
            }
        }
        else {
            if(grid[i1][j1] == 1){
                curr++;
            }
            if(grid[i2][j2] == 1){
                curr++;
            }
        }

        auto [a, ab] = x(grid, i1+1, j1  , i2+1, j2  , dp);
        auto [b, bb] = x(grid, i1  , j1+1, i2  , j2+1, dp);
        auto [c, cb] = x(grid, i1  , j1+1, i2+1, j2  , dp);
        auto [d, db] = x(grid, i1+1, j1  , i2  , j2+1, dp);

        bool didGotToEnd = (ab||bb||cb||db);
        int maxi = 0;
        if(ab) maxi = max(maxi, a);
        if(bb) maxi = max(maxi, b);
        if(cb) maxi = max(maxi, c);
        if(db) maxi = max(maxi, d);
        if(!didGotToEnd) curr = 0;
        dp[s] = {maxi+curr, didGotToEnd};
        return {maxi+curr, didGotToEnd};
    }

        // cout << i1 << "," << j1 << "  " << i2 << "," << j2 << ": " << "{" << maxi << "," << didGotToEnd << endl;
    
    int cherryPickup(vector<vector<int>>& grid) {
        n = grid.size();
        m = grid[0].size();
        if(grid[n-1][m-1] == -1 || grid[0][0] == -1){
            return 0;
        }

        unordered_map<string, pair<int, bool>> dp;
        auto w = x(grid, 0, 0, 0, 0, dp);
        return w.first;
    }
};
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