<p>Given an unsorted array of integers <code>nums</code>, return <em>the length of the longest consecutive elements sequence.</em></p>

<p>You must write an algorithm that runs in&nbsp;<code>O(n)</code>&nbsp;time.</p>

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

<pre>
<strong>Input:</strong> nums = [100,4,200,1,3,2]
<strong>Output:</strong> 4
<strong>Explanation:</strong> The longest consecutive elements sequence is <code>[1, 2, 3, 4]</code>. Therefore its length is 4.
</pre>

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

<pre>
<strong>Input:</strong> nums = [0,3,7,2,5,8,4,6,0,1]
<strong>Output:</strong> 9
</pre>

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

<ul>
	<li><code>0 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>-10<sup>9</sup> &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>
</ul>

from collections import defaultdict

class Solution:
    def longestConsecutive(self, nums: List[int]) -> int:
        """
        Example:
        nums = [100, 4, 200, 1, 3, 2]
        """
        if not nums or len(nums)==0:
            return 0

        # O(n): The candidates for the first element
        set_nums = set(nums)
        set_starts = set()
        starts = set([num for num in nums if num-1 not in set_nums])
        
        #print(f"starts={starts}")

        max_cnt = 1
        for start in starts:
            cnt = 1
            
            while start + cnt in set_nums:
                cnt += 1
            max_cnt = max(cnt, max_cnt)

        return max_cnt
        
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