Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow from the statements.

Statements:

1. All parakeets are cuckoos.

2. All cuckoos are rabbits.

3. All rabbits are snakes.

Conclusions:

I. All parakeets are snakes.

II. All snakes are cuckoos.

III. All rabbits are parakeets.