题目描述

Mirko and Slavko are spending their free time playing with polygons and watching a new season of The Biggest Loser. Mirko recently drew a convex polygon with an even number of vertices $N$. Slavko then considered each pair of oposite sides (two sides are opposite if there are $\dfrac N2 - 1$ sides between them), drew straight lines that lie on those sides and colored them along with the part of the plane that lies between them and contains the polygon. Finally, Mirko found a set of $Q$ points and decided to challenge Slavko to answer for each point whether it lies in the colored or uncolored part of the plane. The new episode of The Biggest Loser is about to start and Slavko doesn’t have the time to answer Mirko’s queries. Can you help him?

输入格式

The first line contains an integer $T$ which is used as a parameter for generating Mirko's queries. This number can be either $0$ or $1$.

The second line contains an even integer $N$ from the task description.

Each of the next $N$ lines contains two integers $X_i, Y_i$ ($0\leq|X_i|,|Y_i|\leq10^9$) which represent one of the polygon's vertices. You can assume that the vertices are given in the counter - clockwise order and that no three successive vertices are collinear.

The next line contains an integer $Q$ from the task description.

Each of the next $Q$ lines contains two integers $A_i, B_i$ ($0\leq|A_i|,|B_i|\leq2\cdot10^{18}$) which are used as parameters for generating the point in the $i$ - th of Mirko's queries.

Let $X_i$ be equal to the number of points in the first $i$ (inclusive) of Mirko's queries that lie in the colored part of the plane. Naturally, $X_0 = 0$. The point of Mirko's $i$ - th query should then be generated as:

$$P_i=(A_i\oplus(T\cdot X_{i - 1}^3),B_i\oplus(T\cdot X_{i - 1}^3)) $$

where $\oplus$ represents the bitwise xor operation.

输出格式

The $i$ - th line of output should contain the word DA (YES in Croatian) if the point from $i$ - th of Mirko's queries lies in the colored part of the plane. Otherwise, the $i$ - th line should contain the word NE (NO in Croatian).

题目大意

Mirko 最近绘制了一个具有偶数个顶点 $n$ 的凸多边形。

Slavko 选出了每组对边（如果两个边之间有 $\dfrac{n}{2}-1$ 边，则这两个边对边），画出位于这些边上的直线，并将它们与位于它们之间、包含多边形的平面部分一起涂上颜色。

最终，Mirko 选择了 $q$ 个点，并决定向 Slavko 询问，问他每个点是否位于有色或无色部分。

The Biggest Loser 节目即将开始，Slavko 没有时间回答 Mirko 的问题。你能帮她吗？

0
4
1 1
5 1
4 3
2 2
4
3 2
2 4
6 2
4 5

DA
NE
DA
NE

0
6
-1 -1
2 -1
3 3
2 4
1 4
-2 1
6
2 2
3 0
1 -6
2 6
-5 5
5 10

DA
DA
NE
NE
NE
NE

1
6
-1 -1
2 -1
3 3
2 4
1 4
-2 1
6
2 2
3 0
1 -6
2 6
-5 5
5 10

DA
DA
DA
NE
NE
NE

提示

数据规模及约定

本题采用捆绑测试。

Subtask	Scores	Constraints
$1$	$20$	$1 \le n, q \le 2000$，$T = 0$
$2$	$30$	$1 \le n, q \le 10^5$，$T = 0$
$3$	$60$	$1 \le n, q \le 10^5$，$T = 1$

此外，对于 $100\%$ 的数据，$0 \le |x_i|, |y_i| \le 10^9, 0 \le |a_i|, |b_i| \le 2 \times 10^{18}$。

说明

本题分值按 COCI 原题设置，满分 $110$。

题目译自 COCI2019-2020 CONTEST #2 T5 Zvijezda。