Problem 3 Two species are sharing planet Kepler-442b: Pisidians and Lydians. Members of either species roam individually. They can run into each other only in pairs (randomly) and whenever any two individuals run into each other, they fight. Since Pisidians are stronger and Lydians have magical powers, the outcome of a fight is always the same: If two Lydians fight, one of the Lydians dies and the other survives. . If two Pisidians fight, both Pisidians die and a new Lydian comes to existence. If a Pisidian and a Lydian fight, the Lydian dies and the Pisidian survives. At the beginning of time, there were m Lydians and n Pisidians on Kepler-442b. Observing that there will be only one individual left on Kepler-442b at eternity, identify the species of the eternal individual as a function of m and/or n. (Hint: Describe the process using a loop and define a loop invariant.)