 So let's take care of that first rule that we just kind of casually we're able to skip over. What happens if I were to come in and I were to do a remove on 40? Now, 40 is my root again, so once again we mark it as my in and we traverse to find my in order predecessor, which happens to be 25 this time. So I would come in and I would remove that 40 and give it 25 just like we would normally do. However, we run into a slight problem because once again, since my X is a black node, we have to look at my sibling. And in this case, you notice that my sibling has two black children, two black children. And so we don't do the same thing that we did before. So you're noticing one of the things that we first do and let me remove sort of that's the wrong color. Let me remove that 25 from there. So where I use a term called double black, make X double black. So the entire premise behind this is this node right here now has too many levels of black in it. If I were to just leave it as is, it would actually sort of count as two. And so in our regard, we want to resolve this issue. So to resolve it, what we do is, as you can see, I've marked it black. And then I'm going to change my sibling now to red. I'm going to take it and it now becomes a red node. And then I'm going to take one of those black levels that I had with X, and I'm actually going to give it to my parents. What this allows me to do. So if I once again recolor my parents now as a black node, if I recolor it as a black node, that means I've stripped it of that additional level of black that needed to get removed, that needed to vanish from it, be taken off of it. And so since it's been removed, that idea that it gets counted as two has also been removed. So again, if we've looked at black depth, I see I have one black node, two black nodes, three, four, one, two, three. Well, this one happens to be blank. Remember, it's a null node. So it's not got any null children. It's sort of just to kind of color over it for a second. It's a null node. So it one, two, three, four, one, two, three, four. Once again, all of my paths happen to be perfectly okay.