1240\. Tiling a Rectangle with the Fewest Squares

Hard

Given a rectangle of size `n` x `m`, return _the minimum number of integer-sided squares that tile the rectangle_.

**Example 1:**

![](https://assets.leetcode.com/uploads/2019/10/17/sample_11_1592.png)

**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:**

![](https://assets.leetcode.com/uploads/2019/10/17/sample_22_1592.png)

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

**Output:** 5

**Example 3:**

![](https://assets.leetcode.com/uploads/2019/10/17/sample_33_1592.png)

**Input:** n = 11, m = 13

**Output:** 6

**Constraints:**

*   `1 <= n, m <= 13`