<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;
    }
    bool isValid2(vector<vector<int>>& grid, int i1, int j1, int i2, int j2) {
        return isValid(grid, i1, j1) && isValid(grid, i2, j2);
    }
    pair<int, bool> x(vector<vector<int>>& grid, int i1, int j1, int i2, int j2,
                      unordered_map<string, pair<int, bool>>& dp) {
        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++;
        }

        int maxi = 0;
        bool didGotToEnd = false;
        if(isValid2(grid, i1+1, j1, i2+1, j2)) {
            auto [a, ab] = x(grid, i1+1, j1, i2+1, j2, dp);
            maxi = max(maxi, a);
            didGotToEnd = (didGotToEnd || ab);
        }
        if(isValid2(grid, i1, j1+1, i2, j2+1)) {
            auto [a, ab] = x(grid, i1, j1+1, i2, j2+1, dp);
            maxi = max(maxi, a);
            didGotToEnd = (didGotToEnd || ab);
        } 
        if(isValid2(grid, i1, j1+1, i2+1, j2)) {
            auto [a, ab] = x(grid, i1, j1+1, i2+1, j2, dp);
            maxi = max(maxi, a);
            didGotToEnd = (didGotToEnd || ab);
        } 
        if(isValid2(grid, i1+1, j1, i2, j2+1)) {
            auto [a, ab] = x(grid, i1+1, j1, i2, j2+1, dp);
            maxi = max(maxi, a);
            didGotToEnd = (didGotToEnd || ab);
        } 

        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;
    }
};
132003