You are given an $n imes n$ integer array fruits where fruits[i][j] represents the number of fruits at cell $(i, j)$.

Three children collect fruits in the grid according to the following rules:

• The first child starts at cell $(0, 0)$ and moves to cell $(i + 1, j + 1)$ at each step.

• The second child starts at cell $(0, n - 1)$ and can move to cell $(i + 1, j - 1)$, $(i + 1, j)$, or $(i + 1, j + 1)$ at each step.

• The third child starts at cell $(n - 1, 0)$ and can move to cell $(i - 1, j + 1)$, $(i, j + 1)$, or $(i + 1, j + 1)$ at each step.

Each child makes exactly $n - 1$ moves and must reach cell $(n - 1, n - 1)$.

When a child visits a cell, they collect all the fruits from that cell. If a cell is visited by more than one child, the fruits in that cell are collected only once.

Return the maximum total number of fruits the three children can collect.

Constraints:

• $2 \leq n ==$ fruits.length $==$ fruits[i].length $\leq 1000$

• $0 \leq$ fruits[i][j] $\leq 1000$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

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Implement your solution in the following coding playground.