The farthest
Given N points on a plane, your task is to handle the following types of queries:
get a b — This query asks you to find and return the maximum value of the expression ax + by for all the points currently in the set.
add x y — This query requires you to add a new point with coordinates (x, y) to the set of points.
Input
You are provided with the integer N (1 ≤ N ≤ 10^5), which represents the initial number of points, followed by the coordinates of these N points. Next, you receive the integer M (1 ≤ M ≤ 10^5), which indicates the number of queries, followed by the queries themselves. The format for these queries is illustrated in the example. All coordinates of the points and the integers a and b are within the range of (-10^9) to (10^9).
Output
For each get query, output a single integer representing the maximum value of ax + by.