<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 {
public:
    int tupleSameProduct(vector<int>& nums) {
        int ans = 0;
        int n = nums.size();
        unordered_map<int, int> mult_cnt;
        for (int i = 0 ; i < n; i++){
            for (int j = i+1 ; j < n; j++){
                mult_cnt[nums[i]*nums[j]]++;
            }
        }

        for (auto it = mult_cnt.begin(); it != mult_cnt.end(); it++){
            cout << it->second << endl;
            ans += 4*((it->second-1)*it->second);
        }

        return ans;
    }

    void tupleSameProductHelper(vector<int>& nums, vector<int>& currentTuple, vector<bool>& used_values, int* cnt) {
        if (currentTuple.size() == 4){
            *cnt += currentTuple[0]*currentTuple[1] == currentTuple[2]*currentTuple[3];
        }

        for (int i = 0; i < (int)nums.size(); i++){
            if (used_values[i]){
                continue;
            }

            currentTuple.push_back(nums[i]);
            used_values[i] = true;
            tupleSameProductHelper(nums, currentTuple, used_values, cnt);
            currentTuple.pop_back();
            used_values[i] = false;
        }
    }
};
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