<p>Given a rectangle of size <code>n</code> x <code>m</code>, return <em>the minimum number of integer-sided squares that tile the rectangle</em>.</p>

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

<p><img alt="" src="https://assets.leetcode.com/uploads/2019/10/17/sample_11_1592.png" style="width: 154px; height: 106px;" /></p>

<pre>
<strong>Input:</strong> n = 2, m = 3
<strong>Output:</strong> 3
<strong>Explanation:</strong> <code>3</code> squares are necessary to cover the rectangle.
<code>2</code> (squares of <code>1x1</code>)
<code>1</code> (square of <code>2x2</code>)</pre>

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

<p><img alt="" src="https://assets.leetcode.com/uploads/2019/10/17/sample_22_1592.png" style="width: 224px; height: 126px;" /></p>

<pre>
<strong>Input:</strong> n = 5, m = 8
<strong>Output:</strong> 5
</pre>

<p><strong class="example">Example 3:</strong></p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2019/10/17/sample_33_1592.png" style="width: 224px; height: 189px;" /></p>

<pre>
<strong>Input:</strong> n = 11, m = 13
<strong>Output:</strong> 6
</pre>

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

<ul>
	<li><code>1 &lt;= n, m &lt;= 13</code></li>
</ul>

class Solution:
    def tilingRectangle(self, n: int, m: int) -> int:
        
        grid = [[False for _ in range(m)] for _ in range(n)]

        def check(x, y, size):
            if x+size > n or y+size > m:
                return False
            for i in range(size):
                for j in range(size):
                    if grid[i+x][j+y]:
                        return False
            return True

        def expr(x, y, size, place):
            for i in range(size):
                for j in range(size):
                    grid[i+x][j+y] = place

        ans = float('inf')
        def func(count):
            nonlocal ans
            if count>ans:
                return
            for i in range(n):
                for j in range(m):
                    if not grid[i][j]:
                        for size in range(min(n-i,m-j), 0, -1):
                            if check(i, j, size):
                                expr(i,j,size,True)
                                func(count+1)
                                expr(i,j,size,False)
                        return
            ans = min(ans, count)

        func(0)
        return ans

        





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