<p>You are given an integer array <code>nums</code> of length <code>n</code> where <code>nums</code> is a permutation of the numbers in the range <code>[0, n - 1]</code>.</p>

<p>You should build a set <code>s[k] = {nums[k], nums[nums[k]], nums[nums[nums[k]]], ... }</code> subjected to the following rule:</p>

<ul>
	<li>The first element in <code>s[k]</code> starts with the selection of the element <code>nums[k]</code> of <code>index = k</code>.</li>
	<li>The next element in <code>s[k]</code> should be <code>nums[nums[k]]</code>, and then <code>nums[nums[nums[k]]]</code>, and so on.</li>
	<li>We stop adding right before a duplicate element occurs in <code>s[k]</code>.</li>
</ul>

<p>Return <em>the longest length of a set</em> <code>s[k]</code>.</p>

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

<pre>
<strong>Input:</strong> nums = [5,4,0,3,1,6,2]
<strong>Output:</strong> 4
<strong>Explanation:</strong> 
nums[0] = 5, nums[1] = 4, nums[2] = 0, nums[3] = 3, nums[4] = 1, nums[5] = 6, nums[6] = 2.
One of the longest sets s[k]:
s[0] = {nums[0], nums[5], nums[6], nums[2]} = {5, 6, 2, 0}
</pre>

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

<pre>
<strong>Input:</strong> nums = [0,1,2]
<strong>Output:</strong> 1
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= nums[i] &lt; nums.length</code></li>
	<li>All the values of <code>nums</code> are <strong>unique</strong>.</li>
</ul>

class Solution:
    def arrayNesting(self, nums: List[int]) -> int:
        res = [0]
        seen = set()
        dp = {}

        def dfs(i, count):
            if i in dp:
                return dp[i]

            if i not in seen:
                seen.add(i)
                dfs(nums[i], count+1)
                seen.remove(i)
            
            res[0] = max(res[0], count)
            dp[i] = res[0]

        
        for i in range(len(nums)):
            dfs(i, 0)
        
        return res[0]
        
        
107248