<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>

def calc_row(row, reverse):
    res = []
    twos = 0
    fives = 0
    for val in (reversed(row) if reverse else row):
        while val % 2 == 0:
            val //= 2
            twos += 1
        while val % 5 == 0:
            val //= 5
            fives += 1
        res.append((twos, fives))
    if reverse:
        res = res[::-1]
    return res
class Solution:
    def maxTrailingZeros(self, grid: List[List[int]]) -> int:
        left_zeros = [calc_row(row, False) for row in grid]
        right_zeros = [calc_row(row, True) for row in grid]
        top_zeros = [calc_row(col, False) for col in zip(*grid)]
        bot_zeros = [calc_row(col, True) for col in zip(*grid)]

        cols = len(grid[0])
        rows = len(grid)

        # try every point on the boundary
        max_top = 0
        for i in range(cols):
            for turn_at in range(rows):
                twos, fives = top_zeros[i][turn_at]
                d2l, d5l = left_zeros[turn_at][i - 1] if i else (0, 0)
                d2r, d5r = right_zeros[turn_at][i + 1] if i + 1 < cols else (0, 0)
                max_top = max(max_top, min(twos + d2l, fives + d5l), min(twos + d2r, fives + d5r))
        max_bot = 0
        for i in range(cols):
            for turn_at in range(rows):
                twos, fives = bot_zeros[i][turn_at]
                d2l, d5l = left_zeros[turn_at][i - 1] if i else (0, 0)
                d2r, d5r = right_zeros[turn_at][i + 1] if i + 1 < cols else (0, 0)
                max_bot = max(max_bot, min(twos + d2l, fives + d5l), min(twos + d2r, fives + d5r))
        return max(max_top, max_bot)
3095