>> Okay. Here's, here's an outline of the, of the problem solution. So we were asked to show that G is less than or equal to H. That's the same thing as showing H minus G is greater than or equal to 0. There's H. Here's minus G. So we, all we have to do is left moving second wins in this game. Now if right moves first, right's only move is to chop this. Now left has a move of chopping this. Now right has now moved leftwards.