<p>You are given a 2D <strong>binary</strong> array <code>grid</code>. Find a rectangle with horizontal and vertical sides with the<strong> smallest</strong> area, such that all the 1&#39;s in <code>grid</code> lie inside this rectangle.</p>

<p>Return the <strong>minimum</strong> possible area of the rectangle.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">grid = [[0,1,0],[1,0,1]]</span></p>

<p><strong>Output:</strong> <span class="example-io">6</span></p>

<p><strong>Explanation:</strong></p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2024/05/08/examplerect0.png" style="padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; width: 279px; height: 198px;" /></p>

<p>The smallest rectangle has a height of 2 and a width of 3, so it has an area of <code>2 * 3 = 6</code>.</p>
</div>

<p><strong class="example">Example 2:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">grid = [[1,0],[0,0]]</span></p>

<p><strong>Output:</strong> <span class="example-io">1</span></p>

<p><strong>Explanation:</strong></p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2024/05/08/examplerect1.png" style="padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; width: 204px; height: 201px;" /></p>

<p>The smallest rectangle has both height and width 1, so its area is <code>1 * 1 = 1</code>.</p>
</div>

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

<ul>
	<li><code>1 &lt;= grid.length, grid[i].length &lt;= 1000</code></li>
	<li><code>grid[i][j]</code> is either 0 or 1.</li>
	<li>The input is generated such that there is at least one 1 in <code>grid</code>.</li>
</ul>

from typing import List

class Solution:
    def minimumArea(self, grid: List[List[int]]) -> int:
        # Initialize variables to track the extremes
        min_row, max_row = float('inf'), float('-inf')
        min_col, max_col = float('inf'), float('-inf')
        
        # Iterate over each cell in the grid
        for i in range(len(grid)):
            for j in range(len(grid[0])):
                if grid[i][j] == 1:
                    # Update the minimum and maximum row indices
                    min_row = min(min_row, i)
                    max_row = max(max_row, i)
                    # Update the minimum and maximum column indices
                    min_col = min(min_col, j)
                    max_col = max(max_col, j)
        
        # Calculate the area of the bounding rectangle
        area = (max_row - min_row + 1) * (max_col - min_col + 1)
        
        return area

# Example usage:
# solution = Solution()
# print(solution.minimumArea([[0,1,0],[1,0,1]]))  # Output: 6
# print(solution.minimumArea([[1,0],[0,0]]))      # Output: 1
46700