<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:
        # Sort the array
        nums.sort()
        
        # Convert the list to a set for efficient lookup
        num_set = set(nums)
        
        # Dictionary to store the length of the longest square streak ending at each number
        dp = {}
        
        for num in nums:
            if num * num in num_set:
                dp[num * num] = dp.get(num, 1) + 1
            else:
                dp[num * num] = 1
        
        # Find the maximum length of the square streak
        max_streak = max(dp.values())
        
        # If the maximum length is 1, it means there is no square streak
        return max_streak if max_streak > 1 else -1

# Example usage:
solution = Solution()
nums = [4, 3, 6, 16, 8, 2]
print(solution.longestSquareStreak(nums))  # Output: 3

nums = [2, 3, 5, 6, 7]
print(solution.longestSquareStreak(nums))  # Output: -1
39600