In the planet Realmamber, recognized heroes are those warriors who had single-handedly vanquished monsters. Each of five Realmamberians, Actaeon, Ceyx, Minos, Nisus, and Pyramus, had accomplished this feat. They defeated one sea serpent, two griffins and two chimaeras.

All Realmamberians are either Knights, who always speak truthfully; Liars, who always speak falsely; Knaves, who make statements that are alternately true and false, but in which order is unknown; or those few Rebels who do not abide by the planet's traditions.

How truthful a Rebel's statements are is unknown, except that they are not the same as those who are Knights, Liars, or Knaves. Thus, a Rebel will never make just one or two statements; he will always make three or more. As to the five heroes, precisely one of them is a Rebel.

In response to a query posited by an inquisitive visitor from a neighboring planet regarding their identity, they say:


Actaeon:

1. Everything Minos states is false.
2. I did not defeat a griffin.
3. Ceyx defeated a griffin.
4. I agree with Nisus' first statement.

Ceyx:

1. I defeated a sea serpent.
2. Minos did not defeat a chimaera.
3. Nisus defeated a chimaera.
4. Actaeon defeated a griffin.

Minos:

1. I agree with Actaeon's first statement.
2. Ceyx did not defeat a chimaera.
3. Actaeon is not a Knight.
4. I defeated a sea serpent.

Nisus:

1. Minos' third statement is false.
2. I defeated a chimaera.
3. Actaeon did not defeat a griffin.
4. Pyramus defeated a chimaera.

Pyramus:

1. Nisus defeated a sea serpent.
2. Minos is a Knave.
3. Actaeon is not a Liar.
4. Ceyx defeated a chimaera.

Based on the abovementioned statements, determine the group of each hero, and what type of monster each defeated.