An algorithm camp holds a two event race. The race has a running leg and a swimming leg. Every participant runs R meters first, then swims S meters. The person who reaches the finish line first wins. If several people reach the finish line at the same moment, all of them are co-winners.
Before the race starts, Seonggwan looks at the records of the N participants. Participant i runs at ri meters per second and swims at si meters per second, so participant i reaches the finish line at time riR+siS seconds.
Seonggwan knows both speeds of every participant, but he does not know R and S. He only knows that R and S are real numbers greater than 0. The winner changes with the choice of R and S, so he wants to know who can win. Participant i can win if there are real numbers R>0 and S>0 that make participant i a winner or a co-winner. Write a program that finds every participant who can win.