<p>You are given a 2D <strong>binary</strong> array <code>grid</code>. You need to find 3 <strong>non-overlapping</strong> rectangles having <strong>non-zero</strong> areas with horizontal and vertical sides such that all the 1&#39;s in <code>grid</code> lie inside these rectangles.</p>

<p>Return the <strong>minimum</strong> possible sum of the area of these rectangles.</p>

<p><strong>Note</strong> that the rectangles are allowed to touch.</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 = [[1,0,1],[1,1,1]]</span></p>

<p><strong>Output:</strong> <span class="example-io">5</span></p>

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

<p><img alt="" src="https://assets.leetcode.com/uploads/2024/05/14/example0rect21.png" style="padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; width: 280px; height: 198px;" /></p>

<ul>
	<li>The 1&#39;s at <code>(0, 0)</code> and <code>(1, 0)</code> are covered by a rectangle of area 2.</li>
	<li>The 1&#39;s at <code>(0, 2)</code> and <code>(1, 2)</code> are covered by a rectangle of area 2.</li>
	<li>The 1 at <code>(1, 1)</code> is covered by a rectangle of area 1.</li>
</ul>
</div>

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

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

<p><strong>Output:</strong> <span class="example-io">5</span></p>

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

<p><img alt="" src="https://assets.leetcode.com/uploads/2024/05/14/example1rect2.png" style="padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; width: 356px; height: 198px;" /></p>

<ul>
	<li>The 1&#39;s at <code>(0, 0)</code> and <code>(0, 2)</code> are covered by a rectangle of area 3.</li>
	<li>The 1 at <code>(1, 1)</code> is covered by a rectangle of area 1.</li>
	<li>The 1 at <code>(1, 3)</code> is covered by a rectangle of area 1.</li>
</ul>
</div>

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

<ul>
	<li><code>1 &lt;= grid.length, grid[i].length &lt;= 30</code></li>
	<li><code>grid[i][j]</code> is either 0 or 1.</li>
	<li>The input is generated such that there are at least three 1&#39;s in <code>grid</code>.</li>
</ul>

class Solution:
    def minimumSum(self, grid: List[List[int]]) -> int:
        def get(a,b,c,d):
            if b<a or d<c:
                return 1e9
            lx,rx,ty,dy=1e9,-1,1e9,-1
            for i in range(a,b+1):
                for j in range(c,d+1):
                    if grid[i][j]:
                        lx=min(lx,j)
                        rx=max(rx,j)
                        ty=min(ty,i)
                        dy=max(dy,i)
            return (rx-lx+1)*(dy-ty+1)
        ans=1e9
        n,m=len(grid),len(grid[0])
        for i in range(n):
            for j in range(m):
                ans=min(ans,get(0,i,0,m-1)+get(i+1,n-1,0,j)+get(i+1,n-1,j+1,m-1))
                ans=min(ans,get(0,i,0,j)+get(0,i,j+1,m-1)+get(i+1,n-1,0,m-1))
                ans=min(ans,get(0,n-1,0,j)+get(0,i,j+1,m-1)+get(i+1,n-1,j+1,m-1))
                ans=min(ans,get(0,n-1,j+1,m-1)+get(0,i,0,j)+get(i+1,n-1,0,j))
        for i in range(n):
            for j in range(i,n):
                ans=min(ans,get(0,i,0,m-1)+get(i+1,j,0,m-1)+get(j+1,n-1,0,m-1))
        for i in range(m):
            for j in range(i,m):
                ans=min(ans,get(0,n-1,0,i)+get(0,n-1,i+1,j)+get(0,n-1,j+1,m-1))
        return ans
4935