<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>

class Solution:
    def minimumArea(self, grid: List[List[int]]) -> int:
        bottom_most = float('-inf')
        top_most = float('inf')
        left_most = float('inf')
        right_most = float('-inf')
        for j,arr in enumerate(grid):
            if 1 in arr:
                bottom_most = max(bottom_most, j)
                top_most = min(top_most, j)


            for i,w in enumerate(arr):
                if w == 1:
                    left_most = min(i, left_most)
                    right_most = max(i, right_most)
        height = (bottom_most - top_most) + 1
        width = (right_most - left_most) + 1
        return height * width

        


            
        
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