Little Rabbit and Little Horse are playing a game called $\textit{Occupying Grids}$. The game is played on a square grid graph which has $m$ dots each row and $n$ dots each column. The players take turns to draw a segment that connects two adjacent dots. Once the four sides of a grid are all drawn, the player who draws the last side of the grid can occupy the grid and $\textbf{immediately}$ get one more chance to draw another segment. (Sometimes two grids can be occupied at the same time, but the player also gets $\textbf{only one}$ more chance to draw.) The game ends when no more segments can be drawn, and the player who occupies more grids will win the game. (Two players occupying the same number of grids results in a tie.) The picture below shows a game in a $3 \times 3$ square grid graph.
Little Rabbit and Little Horse both play the game for the first time. So in the beginning, they just draw the segments willy-nilly without any strategies. But after $k$ steps, they are surprised to find that each grid has $\textbf{at least 2}$ sides that are drawn. Little Rabbit wants to know whether he can win the game if both players play optimally from now on.
Little Rabbit cannot solve the problem, so he turns to you and shows you the $k$ steps $\textbf{in order}$. But he forgets to note down which player each step belongs to, so you need to judge by yourself. The only thing you know is that the first step belongs to Little Rabbit.
Please note that the $k$ steps given should strictly follow the rules. For example, if one player occupies a grid in some step, then the next step also belongs to him.