human
I found an interesting problem on https://leetcode.com/problems/tiling-a-rectangle-with-the-fewest-squares/:
Given a rectangle of size n x m, find the minimum number of integer-sided squares that tile the rectangle.
 
Example 1:

Input: n = 2, m = 3
Output: 3
Explanation: 3 squares are necessary to cover the rectangle.
2 (squares of 1x1)
1 (square of 2x2)
Example 2:

Input: n = 5, m = 8
Output: 5

Example 3:

Input: n = 11, m = 13
Output: 6

 
Constraints:

1 <= n <= 13
1 <= m <= 13

I tried it in Python, but could not do it. Can you solve it?
assistant
#Here is Python program to find the minimum number of integer-sided squares that tile the rectangle.

class Solution:
    def tilingRectangle(self, n: int, m: int) -> int:
        if m == n:
            return 1
        
        if n > m:
            m,n = n,m
        
        h_i = [0]*n
        
        visited = {}
        
        res = [m*n]
        
        def dfs(height, cnt):
            if cnt > res[0]:
                return
            
            status = tuple(height)
            if status in visited and visited[status] <= cnt:
                return
            visited[status] = cnt
            complete = True
            start_j = -1
            lowest_h = m+1
            
            for j in range(n):
                if height[j] < m:
                    complete = False
                if height[j] < lowest_h:
                    start_j = j
                    lowest_h = height[j]
            
            if complete:
                res[0] = min(res[0], cnt)
                return
            
            j = start_j
            while j < n and height[j] == lowest_h:
                j += 1
            max_l = min(j-start_j, m-lowest_h)
            
            for l in range(max_l, 0, -1):
                next_h = list(height)
                for k in range(l):
                    next_h[start_j+k] += l
                dfs(next_h, cnt+1)
        
        dfs(h_i, 0)
        return res[0]