<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>

from typing import List
from collections import defaultdict
import math

class Solution:
    def longestSquareStreak(self, nums: List[int]) -> int:
        nums_sorted = sorted(set(nums))
        dp = defaultdict(int)
        count_1s = nums.count(1)
        max_chain = 0

        for x in nums_sorted:
            if x == 1:
                dp[x] = count_1s
                if count_1s >= 2:
                    max_chain = max(max_chain, count_1s)
            else:
                sqrt_x = math.isqrt(x)
                if sqrt_x * sqrt_x == x and sqrt_x in dp:
                    dp[x] = dp[sqrt_x] + 1
                    max_chain = max(max_chain, dp[x])
                else:
                    dp[x] = 1

        if count_1s >= 2:
            max_streak = max(max_streak, count_1s)
        else:
            max_streak = max_chain

        return max_streak if max_streak >= 2 else -1
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