<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]:
        if len(changed) % 2 != 0:
            return []
        lookup = {}
        result = []
        for n in changed:
            if n in lookup:
                lookup[n] += 1
            else:
                lookup[n] = 1
        for n in sorted(changed):
            if n not in lookup:
                continue
            
            if n == 0:
                if lookup[0] % 2 == 0:
                    lookup[0] -= 2
                    if lookup[0] == 0:
                        del lookup[0]
                    result.append(0)
                else:
                    return []

            elif 2 * n in lookup:
                lookup[2 * n] -= 1
                lookup[n] -= 1
                if lookup[2 * n] == 0:
                    del lookup[2 * n]
                if lookup[n] == 0:
                    del lookup[n]
                result.append(n)
                continue
            else:
                return []
        
        return result
        
        

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