Animal Feeding Objective Give practice with Sorting in C. Give practice with Binary Search in C. Give practice with Heaps in C. Story Your employees have too many mangos. The mangos go bad after some time and leave a sticky, smelly residue. The park is beginning to look and smell like a pig sty every day. Luckily, you have intercepted the communications with the local mango providers and your employees. Now you know in advance when the mangos arrive for the next year. Additionally, you can estimate when each shipment spoils based on the provider. Your animals can consume food at a constant, non-negative, real rate (in pounds per minute). The more animals you have the higher this rate, but the more it will cost to maintain the park. Your objective is to find out the smallest rate at which the animals need to be able to consume food such that no amount of mango spoils in the upcoming year. You can assume that if there are no mangos in your park, then the animals will instead eat some of the other non-perishable food your park has. Problem Given the shipment description of all the mangos (arrival time, spoil time, and size in pounds). Determine the smallest rate the animals in your park can consume food such that none of the mangos spoil. Input Input will begin with a line containing 1 integer, \( n(1 \leq n \leq 200,000) \), representing the number of shipments of mangos. The following \( \mathrm{n} \) lines will contain the description of a single mango shipment. The mango shipment description will consist of a line with 3 integers, \( T_{s}, T_{n} \) and \( S\left(1 \leq T_{a}