<p>Given an integer array <code>nums</code>, return <em>the number of all the <strong>arithmetic subsequences</strong> of</em> <code>nums</code>.</p>

<p>A sequence of numbers is called arithmetic if it consists of <strong>at least three elements</strong> and if the difference between any two consecutive elements is the same.</p>

<ul>
	<li>For example, <code>[1, 3, 5, 7, 9]</code>, <code>[7, 7, 7, 7]</code>, and <code>[3, -1, -5, -9]</code> are arithmetic sequences.</li>
	<li>For example, <code>[1, 1, 2, 5, 7]</code> is not an arithmetic sequence.</li>
</ul>

<p>A <strong>subsequence</strong> of an array is a sequence that can be formed by removing some elements (possibly none) of the array.</p>

<ul>
	<li>For example, <code>[2,5,10]</code> is a subsequence of <code>[1,2,1,<strong><u>2</u></strong>,4,1,<u><strong>5</strong></u>,<u><strong>10</strong></u>]</code>.</li>
</ul>

<p>The test cases are generated so that the answer fits in <strong>32-bit</strong> integer.</p>

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

<pre>
<strong>Input:</strong> nums = [2,4,6,8,10]
<strong>Output:</strong> 7
<strong>Explanation:</strong> All arithmetic subsequence slices are:
[2,4,6]
[4,6,8]
[6,8,10]
[2,4,6,8]
[4,6,8,10]
[2,4,6,8,10]
[2,6,10]
</pre>

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

<pre>
<strong>Input:</strong> nums = [7,7,7,7,7]
<strong>Output:</strong> 16
<strong>Explanation:</strong> Any subsequence of this array is arithmetic.
</pre>

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

<ul>
	<li><code>1&nbsp; &lt;= nums.length &lt;= 1000</code></li>
	<li><code>-2<sup>31</sup> &lt;= nums[i] &lt;= 2<sup>31</sup> - 1</code></li>
</ul>

class Solution:
    def numberOfArithmeticSlices(self, nums: List[int]) -> int:
        two_or_more = {}
        counts = {}
        n = len(nums)
        total = 0
        for idx in range(n - 1, -1, -1):
            # print("*********")
            # print(total)
            # print(two_or_more)
            curr = nums[idx]
            updates = []
            for pidx in range(idx):
                prev = nums[pidx]
                diff = curr - prev
                update = 0
                if curr + diff in counts:
                    update += counts[curr + diff]
                if (curr + diff, diff) in two_or_more:
                    update += two_or_more[(curr + diff, diff)]
                # print(idx, pidx, update)
                total += update
                updates.append((curr, diff, update))

            if curr not in counts:
                counts[curr] = 0
            counts[curr] += 1

            seen = set()
            for val, incr, num_new in updates:
                if (val, incr) in seen:
                    continue
                seen.add((val, incr))
                if (val, incr) not in two_or_more:
                    two_or_more[(val, incr)] = num_new
                else:
                    two_or_more[(val, incr)] += num_new
        
        return total
         
            


                
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