<p>You are given an integer array <code>nums</code>. A subsequence of <code>nums</code> is called a <strong>square streak</strong> if:</p>

<ul>
	<li>The length of the subsequence is at least <code>2</code>, and</li>
	<li><strong>after</strong> sorting the subsequence, each element (except the first element) is the <strong>square</strong> of the previous number.</li>
</ul>

<p>Return<em> the length of the <strong>longest square streak</strong> in </em><code>nums</code><em>, or return </em><code>-1</code><em> if there is no <strong>square streak</strong>.</em></p>

<p>A <strong>subsequence</strong> is an array that can be derived from another array by deleting some or no elements without changing the order of the remaining elements.</p>

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

<pre>
<strong>Input:</strong> nums = [4,3,6,16,8,2]
<strong>Output:</strong> 3
<strong>Explanation:</strong> Choose the subsequence [4,16,2]. After sorting it, it becomes [2,4,16].
- 4 = 2 * 2.
- 16 = 4 * 4.
Therefore, [4,16,2] is a square streak.
It can be shown that every subsequence of length 4 is not a square streak.
</pre>

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

<pre>
<strong>Input:</strong> nums = [2,3,5,6,7]
<strong>Output:</strong> -1
<strong>Explanation:</strong> There is no square streak in nums so return -1.
</pre>

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

<ul>
	<li><code>2 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>2 &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution:
    def longestSquareStreak(self, nums: List[int]) -> int:
        # Convert the list to a set to remove duplicates and allow O(1) lookups
        s = set(nums)
        
        # Sort the unique numbers and initialize the answer to 0
        nums, ans = sorted(s), 0
        
        # Prune the set to only include numbers n such that n % 4 == 0 or n % 4 == 1
        # This is because only these numbers can potentially be part of a square streak
        s = {n for n in s if n % 4 < 2}

        # Iterate over each number in the sorted list
        for n in nums:
            # Start a potential square streak with the current number
            square, tally = n * n, 1

            # Continue the streak as long as the square of the current number is in the set
            while square in s:
                # Remove the square from the set to avoid reprocessing
                s.remove(square)
                # Increment the tally for the current streak
                tally += 1
                # Move to the next square in the streak
                square *= square

            # Update the answer with the maximum streak length found
            ans = max(ans, tally)
   
        # Return the length of the longest square streak if it's at least 2, otherwise return -1
        return ans if ans > 1 else -1
497