Consider a setting in which player $1$ moves first by choosing among three actions: a$,$ b$,$ and c$.$ After observing the choice of player $1,$ player $2$ chooses among two actions: x and y$.$ Consider the following three variants as to what player $3$ can do and what she knows when she moves:

If player $1$ chose a$,$ then player $3$ selects among two actions: high and low. Player $3$ knows player $2$s choice when she moves. Write down the extensive form of this setting. $($You can ignore payoffs.$)$

If player $1$ chose a$,$ then player $3$ selects among two actions: high and low. Player $3$ does not know player $2$s choice when she moves. Write down the extensive form of this setting. $($You can ignore payoffs.$)$

If player $1$ chose either a or b$,$ then player $3$ selects among two actions: high and low. Player $3$ observes the choice of player $2,$ but not that of player $1.$ Write down the extensive form of this setting. $($You can ignore payoffs.$)$