<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>

class Solution:
    def maxTrailingZeros(self, grid: List[List[int]]) -> int:
        m=len(grid)
        n=len(grid[0])
        grid1=[]
        grid2=[]
        for i in range(m):
            for j in range(n):
                value=[0,0]
                while grid[i][j]%5==0:
                    grid[i][j]//=5
                    value[0]+=1
                while grid[i][j]%2==0:
                    grid[i][j]//=2
                    value[1]+=1
                grid[i][j]=value
        for i in range(m):
            value1=[]
            value2=[]
            for j in range(n):
                value1.append([grid[i][j][0],grid[i][j][1]])
                value2.append([grid[i][j][0],grid[i][j][1]])
            grid1.append(value1)
            grid2.append(value2)
        for i in range(m):
            for j in range(1, n):
                grid1[i][j][0]+=grid1[i][j-1][0]
                grid1[i][j][1]+=grid1[i][j-1][1]
        for j in range(n):
            for i in range(1, m):
                grid2[i][j][0]+=grid2[i-1][j][0]
                grid2[i][j][1]+=grid2[i-1][j][1]
        maximum=0
        for i in range(m):
            maximum=max([maximum, min(grid1[i][-1])])
        for j in range(n):
            maximum=max([maximum, min(grid2[-1][j])])
        for i in range(m):
            for j in range(n):
                value1=[0,0]
                value2=[0,0]
                value3=[0,0]
                value4=[0,0]
                value1[0]=grid1[i][j][0]+grid2[i][j][0]-grid[i][j][0]
                value1[1]=grid1[i][j][1]+grid2[i][j][1]-grid[i][j][1]
                value2[0]=grid1[i][-1][0]-grid1[i][j][0]+grid2[i][j][0]
                value2[1]=grid1[i][-1][1]-grid1[i][j][1]+grid2[i][j][1]
                value3[0]=grid1[i][-1][0]-grid1[i][j][0]+grid2[-1][j][0]-grid2[i][j][0]+grid[i][j][0]
                value3[1]=grid1[i][-1][1]-grid1[i][j][1]+grid2[-1][j][1]-grid2[i][j][1]+grid[i][j][1]
                value4[0]=grid1[i][j][0]+grid2[-1][j][0]-grid2[i][j][0]
                value4[1]=grid1[i][j][1]+grid2[-1][j][1]-grid2[i][j][1]
                maximum=max([maximum, min(value1), min(value2), min(value3), min(value4)])
        return maximum

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