<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:
        def isSqr(x):
            r = int(x**(0.5))
            return (r*r == x)
        validOptions = []
        for i in range(1,n+1):
            if isSqr(i): validOptions.append(i)
        # self.Min = float('inf')
        self.Dict = {}
        def rec(s):
            if s > n:
                return float('inf')
            if s == n:
                return 0
            # key = str(s)+'*'+str(c)
            if s in self.Dict:
                return self.Dict[s]
            Min = float('inf') 
            for j in validOptions:
                # self.Dict[key] = True
                Min = min(Min,rec(s+j))
            self.Dict[s] = Min + 1
            return self.Dict[s]
        return rec(0)
        # return self.Min
23288