<p>Given the <code>root</code> of a binary tree, return <em>the same tree where every subtree (of the given tree) not containing a </em><code>1</code><em> has been removed</em>.</p>

<p>A subtree of a node <code>node</code> is <code>node</code> plus every node that is a descendant of <code>node</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://s3-lc-upload.s3.amazonaws.com/uploads/2018/04/06/1028_2.png" style="width: 500px; height: 140px;" />
<pre>
<strong>Input:</strong> root = [1,null,0,0,1]
<strong>Output:</strong> [1,null,0,null,1]
<strong>Explanation:</strong> 
Only the red nodes satisfy the property &quot;every subtree not containing a 1&quot;.
The diagram on the right represents the answer.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://s3-lc-upload.s3.amazonaws.com/uploads/2018/04/06/1028_1.png" style="width: 500px; height: 115px;" />
<pre>
<strong>Input:</strong> root = [1,0,1,0,0,0,1]
<strong>Output:</strong> [1,null,1,null,1]
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://s3-lc-upload.s3.amazonaws.com/uploads/2018/04/05/1028.png" style="width: 500px; height: 134px;" />
<pre>
<strong>Input:</strong> root = [1,1,0,1,1,0,1,0]
<strong>Output:</strong> [1,1,0,1,1,null,1]
</pre>

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

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 200]</code>.</li>
	<li><code>Node.val</code> is either <code>0</code> or <code>1</code>.</li>
</ul>