<p>Given an array <code>nums</code> of integers, return <em>the length of the longest arithmetic subsequence in</em> <code>nums</code>.</p>

<p><strong>Note</strong> that:</p>

<ul>
	<li>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.</li>
	<li>A sequence <code>seq</code> is arithmetic if <code>seq[i + 1] - seq[i]</code> are all the same value (for <code>0 &lt;= i &lt; seq.length - 1</code>).</li>
</ul>

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

<pre>
<strong>Input:</strong> nums = [3,6,9,12]
<strong>Output:</strong> 4
<strong>Explanation: </strong> The whole array is an arithmetic sequence with steps of length = 3.
</pre>

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

<pre>
<strong>Input:</strong> nums = [9,4,7,2,10]
<strong>Output:</strong> 3
<strong>Explanation: </strong> The longest arithmetic subsequence is [4,7,10].
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [20,1,15,3,10,5,8]
<strong>Output:</strong> 4
<strong>Explanation: </strong> The longest arithmetic subsequence is [20,15,10,5].
</pre>

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

<ul>
	<li><code>2 &lt;= nums.length &lt;= 1000</code></li>
	<li><code>0 &lt;= nums[i] &lt;= 500</code></li>
</ul>

class Solution:
    def longestArithSeqLength(self, nums: List[int]) -> int:
        n = len(nums)
        if n <= 2:
            return n
        
        result = 2
        maxVal = max(nums)
        minVal = min(nums)
        all_deltas = set()
        for i in range(n):
            if n - i + 1 <= result:
                break
                
            all_deltas.clear()
            for j in range(i+1, n):                
                curr = nums[j]
                delta = nums[i] - nums[j]
                if delta in all_deltas:
                    continue
                all_deltas.add(delta)
                count = 2
                pos = j
                nextVal = curr - delta
                while nextVal <= maxVal and nextVal >= minVal:
                    try:
                        pos = nums.index(nextVal, pos + 1)
                        count += 1                    
                        curr = nextVal
                        nextVal = curr - delta
                    except ValueError:
                        break

                if count > result:
                    result = count

        return result
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