<p>An integer array <code>original</code> is transformed into a <strong>doubled</strong> array <code>changed</code> by appending <strong>twice the value</strong> of every element in <code>original</code>, and then randomly <strong>shuffling</strong> the resulting array.</p>

<p>Given an array <code>changed</code>, return <code>original</code><em> if </em><code>changed</code><em> is a <strong>doubled</strong> array. If </em><code>changed</code><em> is not a <strong>doubled</strong> array, return an empty array. The elements in</em> <code>original</code> <em>may be returned in <strong>any</strong> order</em>.</p>

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

<pre>
<strong>Input:</strong> changed = [1,3,4,2,6,8]
<strong>Output:</strong> [1,3,4]
<strong>Explanation:</strong> One possible original array could be [1,3,4]:
- Twice the value of 1 is 1 * 2 = 2.
- Twice the value of 3 is 3 * 2 = 6.
- Twice the value of 4 is 4 * 2 = 8.
Other original arrays could be [4,3,1] or [3,1,4].
</pre>

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

<pre>
<strong>Input:</strong> changed = [6,3,0,1]
<strong>Output:</strong> []
<strong>Explanation:</strong> changed is not a doubled array.
</pre>

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

<pre>
<strong>Input:</strong> changed = [1]
<strong>Output:</strong> []
<strong>Explanation:</strong> changed is not a doubled array.
</pre>

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

<ul>
	<li><code>1 &lt;= changed.length &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= changed[i] &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution {
public:
    // vector<int> findOriginalArray(vector<int>& changed) {
    //     multiset<int> ms;
    //     for(int i=0;i<changed.size();i++) ms.insert(changed[i]);
    //     vector<int> ans;
    //     for(auto ele : ms){
    //         if(ms.find(ele*2)!=ms.end()){
    //             ans.push_back(ele);
    //             ms.erase(ele);
    //             ms.erase(ele*2);
    //         }
    //         else if(ms.find(ele/2)!=ms.end() && ele%2==0){
    //             ans.push_back(ele/2);
    //             ms.erase(ele/2);
    //             ms.erase(ele);
    //         }
    //     }
    //     if(ans.size()==changed.size()/2){
    //         return ans;
    //     }
    //     return {};
    // }
    vector<int> findOriginalArray(vector<int>& changed) {
    multiset<int> ms(changed.begin(), changed.end());
    vector<int> ans;

    while (!ms.empty()) {
        int ele = *ms.begin();
        ms.erase(ms.begin());

        if (ms.find(ele * 2) != ms.end()) {
            ans.push_back(ele);
            ms.erase(ms.find(ele * 2));
        }
        else if (ele % 2 == 0 && ms.find(ele / 2) != ms.end()) {
            ans.push_back(ele / 2);
            ms.erase(ms.find(ele / 2));
        }
        else {
            return {};
        }
    }

    if (ans.size() == changed.size() / 2) {
        return ans;
    }

    return {};
}

};
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