Score : $300$ points

问题陈述

在二维坐标平面上，其中$x$轴朝右方向，$y$轴朝上方向。

在此平面内，有一个不自相交的四边形。其四个顶点的坐标按照逆时针顺序分别为 $(A_x,A_y)$, $(B_x,B_y)$, $(C_x,C_y)$, 以及 $(D_x,D_y)$。

确定这个四边形是否为凸四边形。

这里，一个四边形是凸四边形当且仅当它的四个内角均小于 $180$ 度。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

Consider a two-dimensional coordinate plane, where the $x$-axis is oriented to the right, and the $y$-axis is oriented upward.

In this plane, there is a quadrilateral without self-intersection.
The coordinates of the four vertices are $(A_x,A_y)$, $(B_x,B_y)$, $(C_x,C_y)$, and $(D_x,D_y)$, in counter-clockwise order.

Determine whether this quadrilateral is convex.

Here, a quadrilateral is convex if and only if all four interior angles are less than $180$ degrees.

Constraints

• $-100 \leq A_x,A_y,B_x,B_y,C_x,C_y,D_x,D_y \leq 100$
• All values in input are integers.
• The given four points are the four vertices of a quadrilateral in counter-clockwise order.
• The quadrilateral formed by the given four points has no self-intersection and is non-degenerate. That is,
  • no two vertices are at the same coordinates;
  • no three vertices are colinear; and
  • no two edges that are not adjacent have a common point.

Input

Input is given from Standard Input in the following format:

$A_x$ $A_y$

$B_x$ $B_y$

$C_x$ $C_y$

$D_x$ $D_y$

Output

If the given quadrilateral is convex, print Yes; otherwise, print No.

Sample Input 1

0 0
1 0
1 1
0 1

Sample Output 1

Yes

The given quadrilateral is a square, whose four interior angles are all $90$ degrees. Thus, this quadrilateral is convex.

Sample Input 2

0 0
1 1
-1 0
1 -1

Sample Output 2

No

The angle $A$ is $270$ degrees. Thus, this quadrilateral is not convex.

update @ 2024/3/10 11:14:34