<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:
        def fact(n):
            if n == 0:
                return 1
            elif n < 2:
                return n
            else:
                return n * fact(n-1)
        
        assert(fact(3) == 6)
        products = dict()
        count = 0
        length = len(nums)
        for i in range(length):
            inum = nums[i]
            for j in range(i+1, length):
                jnum = nums[j]
                prod = inum * jnum
                products[prod] = products.get(prod, 0) + 1
        for n in products:
            x = products[n]
            if x >= 2:
                count += 8 * fact(x)/(2 * fact(x - 2))
                
        return int(count)
        
45600