Fewest Integer Squares Tiling a Rectangle

### Problem Tile an n-by-m rectangle completely with integer-sided squares, without overlaps or uncovered regions. Return the smallest number of squares. A solution may use different square sizes and need not arise from repeatedly cutting the rectangle into two rectangles. ```cpp class Solution { public: int tilingRectangle(int n, int m); }; ``` ### Examples **Example 1:** ```text Input: n = 2, m = 4 Output: 2 Explanation: Two2-by-2 squares tile it. One square cannot equal a nonsquare rectangle. ``` **Example 2:** ```text Input: n = 1, m = 5 Output: 5 Explanation: The height permits only1-by-1 squares, so five are necessary. ``` ### Constraints - Both rectangle dimensions are integers in `[1,13]`. ### Contract considerations Only the minimum count is returned. Every tiling must cover the rectangle without overlaps; no particular construction is prescribed. ```hint Read the boundary condition May tiles have different side lengths, and must they cover every part of the rectangle exactly once? ``` ### Boundary reminders Only the minimum count is returned. Every tiling must cover the rectangle without overlaps; no particular construction is prescribed.