<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 {
public:
    bool issquare(int num) {
        if (num == 1) return true;
        int low = 1, high = num / 2;
        while (low <= high) {
            int mid = low + (high - low) / 2;
            long long square = static_cast<long long>(mid) * mid; // Avoid overflow
            if (square == num) return true;
            if (square > num) high = mid - 1;
            else low = mid + 1;
        }
        return false;
    }

    int numSquares(int n) {
        int minCount = n; // Initialize with a large value (worst case)
        for (int i = 1; i * i <= n; i++) { // Iterate over all possible squares less than or equal to n
            if (issquare(i * i)) {
                int remainder = n;
                int cnt = 0;
                while (remainder >= i * i) {
                    remainder -= i * i;
                    cnt++;
                }
                // After reducing with this square, try to reduce remainder further with smaller squares
                if (remainder > 0) {
                    cnt += numSquares(remainder); // Recursively solve for the remainder
                }
                minCount = min(minCount, cnt);
            }
        }
        return minCount;
    }

};
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