<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 findSquare(num):
            if num == 1: return 1
            l = 1
            r = num // 2
            closest = -1
            while l <= r:
                mid = (l+r) // 2
                square = mid * mid
                if square == num:
                    return mid
                elif square > num:
                    r = mid - 1
                else:
                    closest = mid
                    l = mid + 1
            return closest
        
        @cache
        def solve(num):
            maxSquare = findSquare(num)
            if maxSquare * maxSquare == num:
                return 1
            if maxSquare == -1:
                return float("inf")
            
            res = float("inf")
            for i in range(maxSquare + 1,0,-1):
                res = min(res, solve(num - i * i))
            
            return 1 + res

        return solve(n)
36743