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.

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.

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.

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.

见题面 Input 部分

见题面 Output 部分