<p>Given two arrays of integers <code>nums1</code> and <code>nums2</code>, return the number of triplets formed (type 1 and type 2) under the following rules:</p>

<ul>
	<li>Type 1: Triplet (i, j, k) if <code>nums1[i]<sup>2</sup> == nums2[j] * nums2[k]</code> where <code>0 &lt;= i &lt; nums1.length</code> and <code>0 &lt;= j &lt; k &lt; nums2.length</code>.</li>
	<li>Type 2: Triplet (i, j, k) if <code>nums2[i]<sup>2</sup> == nums1[j] * nums1[k]</code> where <code>0 &lt;= i &lt; nums2.length</code> and <code>0 &lt;= j &lt; k &lt; nums1.length</code>.</li>
</ul>

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

<pre>
<strong>Input:</strong> nums1 = [7,4], nums2 = [5,2,8,9]
<strong>Output:</strong> 1
<strong>Explanation:</strong> Type 1: (1, 1, 2), nums1[1]<sup>2</sup> = nums2[1] * nums2[2]. (4<sup>2</sup> = 2 * 8). 
</pre>

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

<pre>
<strong>Input:</strong> nums1 = [1,1], nums2 = [1,1,1]
<strong>Output:</strong> 9
<strong>Explanation:</strong> All Triplets are valid, because 1<sup>2</sup> = 1 * 1.
Type 1: (0,0,1), (0,0,2), (0,1,2), (1,0,1), (1,0,2), (1,1,2).  nums1[i]<sup>2</sup> = nums2[j] * nums2[k].
Type 2: (0,0,1), (1,0,1), (2,0,1). nums2[i]<sup>2</sup> = nums1[j] * nums1[k].
</pre>

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

<pre>
<strong>Input:</strong> nums1 = [7,7,8,3], nums2 = [1,2,9,7]
<strong>Output:</strong> 2
<strong>Explanation:</strong> There are 2 valid triplets.
Type 1: (3,0,2).  nums1[3]<sup>2</sup> = nums2[0] * nums2[2].
Type 2: (3,0,1).  nums2[3]<sup>2</sup> = nums1[0] * nums1[1].
</pre>

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

<ul>
	<li><code>1 &lt;= nums1.length, nums2.length &lt;= 1000</code></li>
	<li><code>1 &lt;= nums1[i], nums2[i] &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution:
    def numTriplets(self, nums1: List[int], nums2: List[int]) -> int:
        def count_products(nums):
            product_count = defaultdict(int)
            n = len(nums)
            for i in range(n):
                for j in range(i + 1, n):
                    product_count[nums[i] * nums[j]] += 1
            return product_count

        count = 0

        # Count products of pairs in nums2
        product_count_nums2 = count_products(nums2)

        # Count valid triplets for nums1
        for num in nums1:
            square = num ** 2
            if square in product_count_nums2:
                count += product_count_nums2[square]

        # Count products of pairs in nums1
        product_count_nums1 = count_products(nums1)

        # Count valid triplets for nums2
        for num in nums2:
            square = num ** 2
            if square in product_count_nums1:
                count += product_count_nums1[square]

        return count
                                
        
37500