741 Cherry Pickup

# 1. Question

In a N x N`grid`representing a field of cherries, each cell is one of three possible integers.
0 means the cell is empty, so you can pass through;
1 means the cell contains a cherry, that you can pick up and pass through;
-1 means the cell contains a thorn that blocks your way.
Your task is to collect maximum number of cherries possible by following the rules below:
Starting at the position (0, 0) and reaching (N-1, N-1) by moving right or down through valid path cells (cells with value 0 or 1);
After reaching (N-1, N-1), returning to (0, 0) by moving left or up through valid path cells;
When passing through a path cell containing a cherry, you pick it up and the cell becomes an empty cell (0);
If there is no valid path between (0, 0) and (N-1, N-1), then no cherries can be collected.
Example 1:
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Input:
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grid = [[0, 1, -1],
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[1, 0, -1],
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[1, 1, 1]]
5
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Output: 5
7
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Explanation:
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The player started at (0, 0) and went down, down, right right to reach (2, 2).
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4 cherries were picked up during this single trip, and the matrix becomes [[0,1,-1],[0,0,-1],[0,0,0]].
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Then, the player went left, up, up, left to return home, picking up one more cherry.
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The total number of cherries picked up is 5, and this is the maximum possible.
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Note:
`grid`is an`N`by`N`2D array, with`1 <= N <= 50`.
Each`grid[i][j]`is an integer in the set`{-1, 0, 1}`.
It is guaranteed that grid[0][0] and grid[N-1][N-1] are not -1.

(1) 4D DP
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