<p>Given an array <code>nums</code> of <strong>distinct</strong> positive integers, return <em>the number of tuples </em><code>(a, b, c, d)</code><em> such that </em><code>a * b = c * d</code><em> where </em><code>a</code><em>, </em><code>b</code><em>, </em><code>c</code><em>, and </em><code>d</code><em> are elements of </em><code>nums</code><em>, and </em><code>a != b != c != d</code><em>.</em></p>

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

<pre>
<strong>Input:</strong> nums = [2,3,4,6]
<strong>Output:</strong> 8
<strong>Explanation:</strong> There are 8 valid tuples:
(2,6,3,4) , (2,6,4,3) , (6,2,3,4) , (6,2,4,3)
(3,4,2,6) , (4,3,2,6) , (3,4,6,2) , (4,3,6,2)
</pre>

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

<pre>
<strong>Input:</strong> nums = [1,2,4,5,10]
<strong>Output:</strong> 16
<strong>Explanation:</strong> There are 16 valid tuples:
(1,10,2,5) , (1,10,5,2) , (10,1,2,5) , (10,1,5,2)
(2,5,1,10) , (2,5,10,1) , (5,2,1,10) , (5,2,10,1)
(2,10,4,5) , (2,10,5,4) , (10,2,4,5) , (10,2,5,4)
(4,5,2,10) , (4,5,10,2) , (5,4,2,10) , (5,4,10,2)
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 1000</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>
	<li>All elements in <code>nums</code> are <strong>distinct</strong>.</li>
</ul>



class Solution:
    def tupleSameProduct(self, nums: List[int]) -> int:
        """
        Returns the number of tuples (a, b, c, d) such that a * b = c * d.
        """
        count = 0
        product_map = defaultdict(list)
        
        # Create a map of products to their corresponding indices
        for i in range(len(nums)):
            for j in range(i + 1, len(nums)):
                product = nums[i] * nums[j]
                product_map[product].append((i, j))
        
        # Count the number of tuples (a, b, c, d) such that a * b = c * d
        for product, indices in product_map.items():
            n = len(indices)
            count += n * (n - 1) // 2
        
        return count * 8
117900