in a solar system of $n$ planets, zorn the world conqueror can invade $m$ planets at a time, but once there are less than $m$ free worlds left, he stops. if he invades $13$ at a time then there are $6$ left, and if he invades $14$ at a time then there are $5$ left. if this solar system has more than $100$ planets, what is the smallest number of planets it could have?