<p>You are given a <code>m x n</code> matrix <code>grid</code>. Initially, you are located at the top-left corner <code>(0, 0)</code>, and in each step, you can only <strong>move right or down</strong> in the matrix.</p>

<p>Among all possible paths starting from the top-left corner <code>(0, 0)</code> and ending in the bottom-right corner <code>(m - 1, n - 1)</code>, find the path with the <strong>maximum non-negative product</strong>. The product of a path is the product of all integers in the grid cells visited along the path.</p>

<p>Return the <em>maximum non-negative product <strong>modulo</strong> </em><code>10<sup>9</sup> + 7</code>. <em>If the maximum product is <strong>negative</strong>, return </em><code>-1</code>.</p>

<p>Notice that the modulo is performed after getting the maximum product.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/23/product1.jpg" style="width: 244px; height: 245px;" />
<pre>
<strong>Input:</strong> grid = [[-1,-2,-3],[-2,-3,-3],[-3,-3,-2]]
<strong>Output:</strong> -1
<strong>Explanation:</strong> It is not possible to get non-negative product in the path from (0, 0) to (2, 2), so return -1.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/23/product2.jpg" style="width: 244px; height: 245px;" />
<pre>
<strong>Input:</strong> grid = [[1,-2,1],[1,-2,1],[3,-4,1]]
<strong>Output:</strong> 8
<strong>Explanation:</strong> Maximum non-negative product is shown (1 * 1 * -2 * -4 * 1 = 8).
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/23/product3.jpg" style="width: 164px; height: 165px;" />
<pre>
<strong>Input:</strong> grid = [[1,3],[0,-4]]
<strong>Output:</strong> 0
<strong>Explanation:</strong> Maximum non-negative product is shown (1 * 0 * -4 = 0).
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 15</code></li>
	<li><code>-4 &lt;= grid[i][j] &lt;= 4</code></li>
</ul>

class Solution:
    def maxProductPath(self, grid):
        rows, cols = len(grid), len(grid[0])
        min_product = [[0] * cols for _ in range(rows)]
        max_product = [[0] * cols for _ in range(rows)]
        min_product[0][0] = max_product[0][0] = grid[0][0]
        for r in range(1, rows):
            min_product[r][0] = max_product[r][0] = min_product[r - 1][0] * grid[r][0]
        for c in range(1, cols):
            min_product[0][c] = max_product[0][c] = min_product[0][c - 1] * grid[0][c]
        for r in range(1, rows):
            for c in range(1, cols):
                if grid[r][c] < 0:
                    min_product[r][c] = max(max_product[r - 1][c], max_product[r][c - 1]) * grid[r][c]
                    max_product[r][c] = min(min_product[r - 1][c], min_product[r][c - 1]) * grid[r][c]
                else:
                    min_product[r][c] = min(min_product[r - 1][c], min_product[r][c - 1]) * grid[r][c]
                    max_product[r][c] = max(max_product[r - 1][c], max_product[r][c - 1]) * grid[r][c]
        max_result = max(min_product[rows - 1][cols - 1], max_product[rows - 1][cols - 1])
        return -1 if max_result < 0 else max_result % (10**9+7)

16600