<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:
    def findOriginalArray(self, changed: list[int]) -> list[int]:
        
        Chains = {}
        freq_t = Counter(changed)
        processed = set()
        print(freq_t)
        
        zero_count = freq_t.pop(0,0)
        if zero_count%2 != 0:
            return []
        else:
            zero_count = zero_count//2
        
        for key in freq_t:
            
            L_key = []
            
            if key not in processed:
                
                while(key not in Chains and key in freq_t):
                    L_key = L_key + [key]
                    processed.add(key)
                    key = 2*key
                
                if key in Chains:
                    L_key = L_key + Chains[key]
                    del Chains[key]
                
                Chains[L_key[0]] = L_key

        for head in Chains:
            for element in Chains[head][:-1]:
                freq_t[2*element] -= freq_t[element]

        ret_list = list(freq_t.elements()) + zero_count*[0]

        if len(ret_list) != len(changed)//2: return []
       
        return ret_list
38000