<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]:
        original_list = []
        num_count_dict = {}
        for item in changed:
            if item in num_count_dict :
                num_count_dict[item] += 1
            else:
                num_count_dict[item] = 1
        num_list = list(set(num_count_dict.keys()))
        num_list.sort()
        for num in num_list:
            if (num_count_dict[num] < 0) or ((num == 0) and (num_count_dict[num]%2!=0)):
                return []
            else: 
                for i in range(num_count_dict[num]):
                    if num==0:
                        if i%2 ==0:
                            original_list.append(num)
                    else:
                        original_list.append(num)
                if (num * 2) in num_count_dict:
                    num_count_dict[(num * 2)] -= num_count_dict[num]
                elif (num_count_dict[num] == 0):
                    continue
                else:
                    return []
        return original_list
                
            
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