277. Heroes

Time limit per test: 1 second(s)
Memory limit: 65536 kilobytes
input: standard
output: standard



In the game 'Heroes of keyboard and mouse' there are some cities at the plane; each city is situated in a point. The player can build some new cities. All the cities are surrounded by a polygonal wall of minimal length. When a city is built, the wall may be rebuilt to include it. Your task is to determine the area inside the wall each time a new city is built. Of course, the cities are in distinct points.

Input
The game starts with three cities with coordinates (x1,y1), (x2,y2) and (x3,y3), which are given in the first line of the input. The initial area inside the wall is non-negative. The second line of the input contains single integer N (1≤ N≤ 100000), being the number of cities to be built. Each of the next N lines contains the coordinates of a city to be built. All the coordinates are integer and do not exceed 108 by absolute value.

Output
The K-th line of the output (1≤ K≤ N) must contain an integer, being the doubled area inside the wall after building K first cities (as listed in the input, not including the first three).

Example(s)
sample input
 
sample output
 
1 0 0 3 3 2
5
1 2
2 1
3 0
2 3
0 1

8
8
12
14
16



Novosibirsk SU Contest #2, by Novosibirsk Team #1