<p>You are given a 2D integer array <code>grid</code> of size <code>m x n</code>, where each cell contains a positive integer.</p>

<p>A <strong>cornered path</strong> is defined as a set of adjacent cells with <strong>at most</strong> one turn. More specifically, the path should exclusively move either <strong>horizontally</strong> or <strong>vertically</strong> up to the turn (if there is one), without returning to a previously visited cell. After the turn, the path will then move exclusively in the <strong>alternate</strong> direction: move vertically if it moved horizontally, and vice versa, also without returning to a previously visited cell.</p>

<p>The <strong>product</strong> of a path is defined as the product of all the values in the path.</p>

<p>Return <em>the <strong>maximum</strong> number of <strong>trailing zeros</strong> in the product of a cornered path found in </em><code>grid</code>.</p>

<p>Note:</p>

<ul>
	<li><strong>Horizontal</strong> movement means moving in either the left or right direction.</li>
	<li><strong>Vertical</strong> movement means moving in either the up or down direction.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/03/23/ex1new2.jpg" style="width: 577px; height: 190px;" />
<pre>
<strong>Input:</strong> grid = [[23,17,15,3,20],[8,1,20,27,11],[9,4,6,2,21],[40,9,1,10,6],[22,7,4,5,3]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> The grid on the left shows a valid cornered path.
It has a product of 15 * 20 * 6 * 1 * 10 = 18000 which has 3 trailing zeros.
It can be shown that this is the maximum trailing zeros in the product of a cornered path.

The grid in the middle is not a cornered path as it has more than one turn.
The grid on the right is not a cornered path as it requires a return to a previously visited cell.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/03/25/ex2.jpg" style="width: 150px; height: 157px;" />
<pre>
<strong>Input:</strong> grid = [[4,3,2],[7,6,1],[8,8,8]]
<strong>Output:</strong> 0
<strong>Explanation:</strong> The grid is shown in the figure above.
There are no cornered paths in the grid that result in a product with a trailing zero.
</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;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= m * n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= grid[i][j] &lt;= 1000</code></li>
</ul>

counter_2 = [0] * 1001
counter_5 = [0] * 1001
counter_2[2] = counter_5[5] = 1
for i in range(3, 1001):
    if i % 2 == 0:
        counter_2[i] = counter_2[i//2] + 1
    if i % 5 == 0:
        counter_5[i] = counter_5[i//5] + 1
class Solution:
    def maxTrailingZeros(self, grid: List[List[int]]) -> int:
        prefix_2 = []
        prefix_5 = []
        for row in grid:
            cur_2 = [0]
            cur_5 = [0]
            for x in row:
                cur_2.append(cur_2[-1] + counter_2[x])
                cur_5.append(cur_5[-1] + counter_5[x])
            prefix_2.append(cur_2)
            prefix_5.append(cur_5)
        ans = 0
        row_2_5 = [[0,0] for _ in grid[0]]
        for i, row in enumerate(grid):
            for j, x in enumerate(row):
                c_2_right = prefix_2[i][-1] - prefix_2[i][j]
                c_5_right = prefix_5[i][-1] - prefix_5[i][j]
                c_2_left = prefix_2[i][j+1]
                c_5_left = prefix_5[i][j+1]
                c_0 = max(min(row_2_5[j][0] + c_2_right, row_2_5[j][1] + c_5_right), min(row_2_5[j][0] + c_2_left, row_2_5[j][1] + c_5_left))
                ans = max(ans, c_0)
                row_2_5[j][0] += counter_2[x]
                row_2_5[j][1] += counter_5[x]
        
        row_2_5 = [[0,0] for _ in grid[0]]
        for i in range(len(grid)-1, -1, -1):
            for j, x in enumerate(grid[i]):
                c_2_right = prefix_2[i][-1] - prefix_2[i][j]
                c_5_right = prefix_5[i][-1] - prefix_5[i][j]
                c_2_left = prefix_2[i][j+1]
                c_5_left = prefix_5[i][j+1]
                c_0 = max(min(row_2_5[j][0] + c_2_right, row_2_5[j][1] + c_5_right), min(row_2_5[j][0] + c_2_left, row_2_5[j][1] + c_5_left))
                ans = max(ans, c_0)
                row_2_5[j][0] += counter_2[x]
                row_2_5[j][1] += counter_5[x]
        return ans
2147