<p>Given an integer <code>n</code>, return <em>the least number of perfect square numbers that sum to</em> <code>n</code>.</p>

<p>A <strong>perfect square</strong> is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, <code>1</code>, <code>4</code>, <code>9</code>, and <code>16</code> are perfect squares while <code>3</code> and <code>11</code> are not.</p>

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

<pre>
<strong>Input:</strong> n = 12
<strong>Output:</strong> 3
<strong>Explanation:</strong> 12 = 4 + 4 + 4.
</pre>

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

<pre>
<strong>Input:</strong> n = 13
<strong>Output:</strong> 2
<strong>Explanation:</strong> 13 = 4 + 9.
</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution:
    def numSquares(self, n: int) -> int:
        min_squares_at = {}
        def get_num_squares(n: int) -> int:
            if n in min_squares_at.keys():
                return min_squares_at[n]
            else:
                possible_squares = [i**2 for i in range(1, n//2+1) if i**2 <= n]
                minimum = n // 1
                for square in possible_squares:
                    if n // square >= minimum:
                        continue
                    new = n // square + get_num_squares(n % square)
                    minimum = new if new < minimum else minimum
                min_squares_at[n] = minimum
                return min_squares_at[n]
        return get_num_squares(n)
18803