CF87E.Mogohu-Rea Idol

A long time ago somewhere in the depths of America existed a powerful tribe governed by the great leader Pinnie-the-Wooh. Once the tribe conquered three Maya cities. Pinnie-the-Wooh grew concerned: there had to be some control over the conquered territories. That's why he appealed to the priests of the supreme god Mogohu-Rea for help.

The priests conveyed the god's will to him: to control these three cities he should put an idol to Mogohu-Rea — that will create a religious field over the cities. However, the idol is so powerful that it can easily drive the people around it mad unless it is balanced by exactly three sacrifice altars, placed one in each city. To balance the idol the altars should be placed so that the center of mass of the system of these three points coincided with the idol. When counting the center of mass consider that all the altars have the same mass.

Now Pinnie-the-Wooh is thinking where to put the idol. He has a list of hills, that are suitable to put an idol there. Help him to identify on which of them you can put an idol without risking to fry off the brains of the cities' population with the religious field.

Each city has a shape of a convex polygon such that no three vertexes lie on a straight line. The cities can intersect. Each altar should be attached to the city through a special ceremony, besides, it must be situated on the city's territory (possibly at the border). Thus, there may be several altars on a city's territory, but exactly one of them will be attached to the city. The altars, the idol and the hills are points on the plane, some of them may coincide.

The hills are taken into consideration independently from each other, the altars' location for different hills may also be different.

很久以前，在美洲大陆的深处，存在着一个由伟大领袖皮尼-伍赫（Pinnie-the-Wooh）统治的强大部落。某次，该部落征服了三座玛雅城市。皮尼-伍赫深感忧虑：必须对这些被征服的领土实施有效管控。因此，他向至高神莫戈胡-雷亚（Mogohu-Rea）的祭司们求助。

祭司们向他传达了神的旨意：为管控这三座城市，须竖立一尊莫戈胡-雷亚神像——此举将在三座城市上空形成一片宗教场。然而，该神像威力过于强大，若不以恰好三座献祭祭坛加以平衡（每座城市各设一座），便极易使周围民众陷入疯狂。为实现神像的平衡，这三座祭坛的位置必须满足：由这三个点构成的质心（center of mass）与神像位置重合。在计算质心时，假设所有祭坛质量相等。

如今，皮尼-伍赫正思索神像应安放于何处。他手头有一份适合作为神像基座的山丘列表。请你帮他判断：在这些山丘中，哪些位置可安全安置神像，而不会因宗教场过强而“烤焦”各城市居民的脑髓。

每座城市均呈凸多边形形状，且其任意三个顶点均不共线。各城市之间可以相互重叠。每座祭坛须通过一场特殊仪式与对应城市绑定；此外，祭坛必须位于该城市的疆域内（边界上亦可）。因此，某座城市的疆域内可能设有多个祭坛，但其中仅有一个将通过仪式与该城市绑定。神像、祭坛及山丘均为平面上的点，其中部分点可能重合。

各山丘被独立考虑，针对不同山丘所选取的祭坛位置也可互不相同。

First follow descriptions of the three cities, divided by empty lines. The descriptions are in the following format:

The first line contains an integer n, which represent the number of the polygon's vertexes (3 ≤ n ≤ 5·104). Next n lines contain two integers x__i, y__i each, they are the coordinates of the polygon's i-th vertex in the counterclockwise order.

After the cities' description follows the integer m (1 ≤ m ≤ 105), which represents the number of hills. Next m lines each contain two integers x__j, y__j, they are the coordinates of the j-th hill.

All the coordinates in the input data do not exceed 5·108 in the absolute value.

首先给出三座城市的描述，城市之间以空行分隔。每座城市的描述格式如下：

第一行包含一个整数 $n$，表示多边形的顶点数（$3 \leq n \leq 5\cdot10^4$）。接下来的 $n$ 行每行包含两个整数 $x_i$、$y_i$，表示该多边形第 $i$ 个顶点的坐标，顶点按逆时针顺序给出。

在三座城市的描述之后，输入一个整数 $m$（$1 \leq m \leq 10^5$），表示山丘的数量。接下来的 $m$ 行每行包含两个整数 $x_j$、$y_j$，表示第 $j$ 座山丘的坐标。

输入数据中所有坐标的绝对值均不超过 $5\cdot10^8$。

For each hill print on a single line "YES" (without the quotes) or "NO" (without the quotes), depending on whether the three sacrifice altars can be put to balance the idol or not.

对于每座山，根据是否能放置三座祭坛以使神像保持平衡，在单独一行输出 “YES”（不带引号）或 “NO”（不带引号）。

For the hill at (2, 1) the altars can be placed at the points (1, 0), (7, 5), ( - 2,  - 2), for the hill at (1, 1) — at the points (0, 0), (6, 4), ( - 3,  - 1). Many other groups of three points can do the trick. There are no suitable points for other hills.

对于位于 $(2,\,1)$ 的山丘，祭坛可以放置在点 $(1,\,0)$、$(7,\,5)$、$(-2,\,-2)$ 处；对于位于 $(1,\,1)$ 的山丘，祭坛可以放置在点 $(0,\,0)$、$(6,\,4)$、$(-3,\,-1)$ 处。许多其他由三个点组成的集合也能满足要求。其余山丘不存在合适的点。