SP1962 CIRCLES - Circles

Little Gary plays the following video game. Circles pop up on the screen and disappear from it. When the screen flashes, Gary can draw a straight line on the screen and win as many points as there are circles intersected by the line. As a born-to-be-winner, Gary wants to maximize his score. Please, help him, and write a program that will determine the maximum number of points he can win each time the screen flashes.

The first line of the input contains _M_ (_1_ ≤ _M_ ≤ _1000_), the number of events during the game. The next _M_ lines contain descriptions of the events, one per line. They can be in one of the following three formats: 1 _x_ _y_ _r_ , representing a circle of radius _r_ popping up with the position of its center at (_x_, _y_) in the plane 2 _i_ , representing a circle _i_ disappearing, where circle _i_ is the _i_th circle that popped up since the beginning of the game; and 3 , representing the screen flashing. _x_, _y_, and _r_ are real numbers with at most two decimals, _-10 $ ^{6} $_ < _x_, _y_, _r_ < _10 $ ^{6} $_ , _r_ > 0. Notes: - A line intersects a circle if it has at least two common points with it. - At any time, no two Circles on the screen have a common point. - At any time, there is no line that "touches" more than two circles (a line touches a circle if they have exactly one common point). - At any time, there are no more than 100 circles on the screen. - Each _i_ determines a circle that is on the screen at the moment of removal. - No circle is removed twice.

Each time the screen flashes, write an integer to a separate line, which is the maximum number of circles Gary can intersect.