<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, n = len(grid), len(grid[0])
      new_grid = [[[0, 0] for _ in range(n)] for _ in range(m)]
      for i in range(m):
        for j in range(n):
          target = grid[i][j]
          count2, count5 = 0, 0
          while target % 2 == 0:
            count2 += 1
            target = target//2
          while target % 5 == 0:
            count5 += 1
            target = target//5
          new_grid[i][j] = [count2, count5]
      verti_grid = [[[0, 0] for _ in range(n)] for _ in range(m)]
      hori_grid = [[[0, 0] for _ in range(n)] for _ in range(m)]
      
      for i in range(m):
        sum2, sum5 = 0, 0
        for j in range(n):
          sum2 += new_grid[i][j][0]
          sum5 += new_grid[i][j][1]
          hori_grid[i][j] = [sum2, sum5]
          
      for j in range(n):
        sum2, sum5 = 0, 0
        for i in range(m):
          sum2 += new_grid[i][j][0]
          sum5 += new_grid[i][j][1]
          verti_grid[i][j] = [sum2, sum5]
        
      res = -sys.maxsize
      
      for i in range(m):
        for j in range(n):
          start2, start5 = hori_grid[i][j][0], hori_grid[i][j][1]
          start2_up, start5_up = start2 + verti_grid[i][j][0] - new_grid[i][j][0], \
                                 start5 + verti_grid[i][j][1] - new_grid[i][j][1]
          start2_down, start5_down = start2 + verti_grid[-1][j][0] - verti_grid[i][j][0], \
                                     start5 + verti_grid[-1][j][1] - verti_grid[i][j][1]
          res = max([min(start2_up, start5_up), min(start2_down, start5_down), res])

      for i in range(m):
        for j in range(n):
          if j != 0:
            start2, start5 = hori_grid[i][-1][0] - hori_grid[i][j-1][0], \
                             hori_grid[i][-1][1] - hori_grid[i][j-1][1]
          else:
            start2, start5 = hori_grid[i][-1][0], hori_grid[i][-1][1]
          start2_up, start5_up = start2 + verti_grid[i][j][0] - new_grid[i][j][0], \
                                 start5 + verti_grid[i][j][1] - new_grid[i][j][1]
          start2_down, start5_down = start2 + verti_grid[-1][j][0] - verti_grid[i][j][0], \
                                     start5 + verti_grid[-1][j][1] - verti_grid[i][j][1]
          res = max([min(start2_up, start5_up), min(start2_down, start5_down), res])
          
      return res
3232